Prove (1+tanx)/(1+cotx)=tanx by algebra

Answers

Answer 1

[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]


Related Questions

Find the values of x and y in the parallelogram.

Answers

Answer:
x = 20
y = 8

In a parallelogram, there are always two pairs of equal sides, where in this question:

Side CD = Side BA
Side DA = Side CB

Use this to find x and y.

CD = BA
15 = x - 5
x = 20 (rearranging to find x)

DA = CB
y = 8

A bag of paper clips contains:
. 9 pink paper clips
• 7 yellow paper clips
• 5 green paper clips
• 4 blue paper clips
A random paper clip is drawn from the bag and replaced 50 times. What is a
reasonable prediction for the number of times a yellow paper clip will be
drawn?

Answers

Answer:

14 times

Step-by-step explanation: add all colors up for total which is 25

since 7 out of the 25 total paper clips are yellow you would have a 7/25 chance of getting yellow after 1 pick.

since you pick and replace 50 times do  (7/25) X 50 which gives you 14 times yellow will be drawn.

14 times
Step-by-step explanation: add all colors
up for total which is 25
since 7 out of the 25 total paper clips are
yellow you would have a 7/25 chance of
getting yellow after 1 pick.
since you pick and replace 50 times do
(7/25) × 50 which gives you 14 times
yellow will be drawn.

liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.

Answers

Answer:

Random sampling

Step-by-step explanation:

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.

Whats 2 plus 0 bc I can't figure it out ......

Answers

The answer to 2 plus 0 is 2

Answer:

this is the hardest one yet gee

Step-by-step explanation:

2 + O = 2

the ratio of the measures of the three angles in a triangle is 9:3:6.
find the measures of the largest angle.

Answers

Step-by-step explanation:

this is how you solve it :)

HELP PLEASE HURRY!!
g(x)
3
f(x) = 4x + 5
-32
#12
Which function has the greatest y-intercept?
3/
h(x)=3 sin(2x + 1)-2

Answers

The second one !!!

I’m pretty sure

Please help will give brainlist and 30 points

Answers

Answer:

1156

Area = base times height

Area = (36-1-1) times (45-10-1)

=1156

please help with all of question 4.​

Answers

Answer:

Step-by-step explanation:

Combine like terms: Like terms have same variable with same power and to combine the like terms, add/subtract the co efficient of the variables.

Perimeter:

      Perimeter = sum of all sides

a) Perimeter of ΔABC = AB + BC + CA

                                    = x + 14 + x + 14 + x + 14

                                    = x + x + x + 14 + 14 + 14    {Combine like terms}

                                   = 3x + 42

b) EF = DI - GH

        = 2x + 3 - x

       = 2x - x + 3

       = x + 3

c) FG = HI - ED

         = 12 + 2x - (x + 5)

         = 12 + 2x - x - 5 {To open the brackets, (-1) is distributed to x and 5}

         = 12 - 5 + 2x - x

         = 7 + x

d) Perimeter of DEFGHI = DE +  EF + FG + GH + HI + ID

                                       =  x + 5 + x + 3 + 7 +x  + x + 12 +2x + 2x + 3

                                       = x +x + x + x + 2x + 2x + 5 + 3 + 7 + 3 + 12  

                                       = 8x + 30

If x and y are adjacent angles, then x and y are ______ acute.

answer choices - always, sometimes, or never.

Answers

Answer:

sometimes

Step-by-step explanation:

adjacent angles are two angles that share a vertex, common side/ray between them, and do not overlap.

only supplementary adjacent angles always add up to 180 degrees,

both x or y could be any angle, as long as they're sharing a common side and vertex.

Guys help me with a) and b) tasks
ANSWER:
a) 40
b) 25
Thanks<3​

Answers

Step-by-step explanation:

there are 2 similar triangles : ABE and DCE

that means they have the same angles, and the scaling factor from one triangle to the other is the same for every side.

and that means that

DE/AE = EC/BE (= DC/AB)

we know that

AE = AD + DE

BE = BC + EC

a.

so, we have actually

DE/(AD+DE) = EC/(BC+EC)

DE/(10+DE) = 8/(2+8) = 8/10 = 4/5

DE = 4(10+DE)/5

5DE = 4(10+DE) = 40 + 4DE

DE = 40 cm

b.

AD/DE = 3/5

BC/EC must be 3/5 too.

15/EC = 3/5

15 = 3EC/5

75 = 3EC

EC = 25 cm

Write a quadratic function with zeroes 6 and 7

Answers

Answer:

f(x) = x² - 13x + 42

Step-by-step explanation:

given zeros are x = 6 and x = 7 then the corresponding factors are

(x - 6) and (x - 7)

the quadratic function is then the product of the factors , that is

f(x) = (x - 6)(x - 7) ← expand using FOIL

     = x² - 13x + 42

1.) Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)

2.) Line segment AB has endpoints B (-3, 0) and A(5, 4). What are the coordinates of the point located 1/4 of the way from B to A?
O (1, -1)
O (1, 2)
O (3, 3)
O (-1, 1)

3.) Line segment AB has endpoints A(1, 8) and B(7, -4). What are the coordinates of the point located 1/6 of the way from A to B?
O (0, 8 2/3
O (2, 6)
O (8 2/3, -3 1/3)
O (6, -3 1/3)

^Please help, ASAP. These were due yesterday, however I am trying to get this done.
BRAINLIEST AND 5 STARS TO CORRECT RESPONSES ONLY! LOTS OF PTS AVAILABLE TO THOSE WHO PARTICIPATE HOWEVER.

Answers

The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

How to find the length of Line Segment?

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

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Students working at a refreshment stand mixed cranberry juice at $0.50 per liter and apple juice at $0.35 per liter to make 120 L of a fruit drink worth $0.40 per liter. How many liters of each did they mix?​

Answers

Answer:

40 L cranberry juice; 80 L apple juice

Step-by-step explanation:

Let x = number of liters of cranberry juice.

The total volume is 120 L, so the volume of apple juice is

120 - x.

The value of the cranberry juice is 0.5x.

The value of the apple juice is 0.35(120 - x).

The value of the mixture is 0.4(120) = 48

The value of the cranberry juice plus the value of the apple juice equals the value of the mixture.

0.5x + 0.35(120 - x) = 48

0.5x + 42 - 0.35x = 48

0.15x = 6

x = 6/0.15

x = 40

120 - x = 120 - 40 = 80

Answer: 40 L cranberry juice; 80 L apple juice

The one-to-one functions g and h are defined as follows.

g = {(-4, 0), (-1, 1), (0, -5), (3,-1)}
h(x) = 2x-13

Answers

What’s the question?

Please help!!! will mark brainliest!!!!!!

Answers

The compound interest will be equal to $13.57.

What is compound interest?

The interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from prior periods is known as compound interest.

The compound interest will be calculated by:-

[tex]CI = P(1+\dfrac{r}{12})^{12t}-P[/tex]

[tex]CI = 250(1+\dfrac{0.053}{12})^{12}-250[/tex]

CI = $13.57

Therefore the compound interest will be equal to $13.57.

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Which answer shows 0.00897 written in scientific notation?
0.897 times 10 Superscript negative 2
8.97 times 10 Superscript negative 3
8.97 times 10 Superscript negative 2
8.97 times 10 Superscript 3

Answers

Answer:

8.97 × 10-3

Step-by-step explanation:

you move the decimal so its a number between 1 and less than 10 so we moved the decimal three spaces.

Answer:

its B

Step-by-step explanation:

someone help me please ​

Answers

The height of the aquarium is h = 18 3/4 yd

Volume of a rectangular box

The formula for calculating the volume of a rectangular box is expressed as

V = lwh

where

l is the length

w is the width

h is the height

Substitute

350 = 20/3 * 14/5 * h

350 = 280/15h

35 = 28/15h

28h = 35 * 15

28h = 525

h = 525/28

h = 18 3/4 yd

Hence the height of the aquarium is h = 18 3/4 yd

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Select the correct answer.


A charity's outreach program is working to provide food and medicine to the people affected by a hurricane. The members drive in a truck from their headquarters at A, as shown in the image, to the locations B, C, D, E, F, G, and H and then go back to their office. What is the total length of their drive?

A.
20 units
B.
30 units
C.
40 units
D.
50 units

Answers

I think the answer is c
I think it is c: 40 units

A certain population of bacteria has an initial population of 225. the bacteria triples every hour. determine the multiplier that would allow you to predict the population of bacteria after 2 hours.

Answers

Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.

What is an exponential function?

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

a is the initial value.b is the growth rate.

In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:

[tex]y = a(3)^x[/tex]

Hence, after 2 hours:

[tex]y = a(3)^2 = 9a[/tex]

Which means that the multiplier is of 9.

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The measures of the angles of △ABC are given by the expressions in the table.

Angle Measure
A 48°
B (6x−28)°
C (2x)°
Find the value of x. Then find the measures of angles B and C.



Enter your answers in the boxes.

x =

​m∠B=​
º

​m∠C=​
º

Answers

Answer:

x = 20  ∠B = 92°  ∠C = 40°

Step-by-step explanation:

The sum of angles of a triangle is 180°.

48 +(6x -28) +2x = 180

8x +20 = 180

8x = 160

x = 20

∠B = (6x -28)° = (6*20 -28)° = 92°

∠C = 2x° = 40°

Answer

X= 20

m<B = 92°

m <C = 40°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So, 48 + 6x-28 +2x = 180

8x+20= 180

8x = 160

So x= 160/8 = 20

Substitute x in the equations:

m<B= 6×20-28= 92°

m<C = 2×20 = 40°

what is the value of u ?

Answers

Step-by-step explanation:

you do know that the sum of all angles in a triangle is always 180° ?

so,

3u + 6u - 18 + u + 18 = 180

10u = 180

u = 18

Is the function f(x) = 1 /x− 1 continuous at x = 1? Explain.

Answers

Faarax Mohammed shirwa search

Answer:

no

Step-by-step explanation:

f(x) = [tex]\frac{1}{x-1}[/tex]

at x = 1

f(1) = [tex]\frac{1}{1-1}[/tex] = [tex]\frac{1}{0}[/tex]

division by zero is undefined, thus there is a discontinuity at x = 1

so f(x) is not continuous at x = 1

Need help with math asap

Answers

[tex]~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan \theta = \dfrac{LN}{LM}\\\\\\\implies \theta = \tan^{-1} \left( \dfrac{LN}{LM} \right)\\\\\\\implies \theta = \tan^{-1} \left(\dfrac{12.81}{7.72} \right)\\\\\\\implies \theta =58.92^{\circ}[/tex]

What is the solution for x in the equation?

x-3/7=2x-25/7

Answers

Step-by-step explanation:

please mark me as brainlest

Answer: x = 4/3

Step-by-step explanation: I just answered the answer

y is inversely proportional to x when x =3, y = 8 work out the value of y when x = 8

Answers

Inversely Proportional

y is inversely proportional to x when x =3, y = 8 work out the value of y when x = 8

y is inversely proportional to x: yx = k, such k is constant

Did you know?

Inversely proportional is also known as inverse variation.

Given:

x = 3y = 8

To determine the constant of variation, substitute the first two given values to the equation of variation.

yx = k(8)(3) = k24 = k

To determine the value of y, substitute the second given value of x including the constant of variation.

x = 8, y = ?yx = 248y = 24y = 24/8y = 3

Answer:

The value of y is 3.

Wxndy~~

A basketball trophy is 1.5 feet tall and casts a 2 foot shadow.
if a basketball hoop casts a 16 foot shadow, how tall is the hoop

Answers

Answer:

12 feet

Step-by-step explanation:

Given that the trophy is 1.5 feet tall which casts a 2 feet shadow and the basketball hoop casts a 16 feet shadow, we can identify the height of the basketball hoop by doing (16÷2)×1.5= 12 feet

Hope this helps with your work

The perimeter of a rectangle is 50 inches. Its width
measures 11 inches. What is its length?
Let x = the length of the rectangle. Choose the equation that represents this
problem.
A. 2x + 22 = 50
B. 2x + 11 = 50
C. x + 11 = 50
D. 2x11 = 50 * don’t try and be funny I need help bad*

Answers

Answer:

50-20 or perimeter-2length

Step-by-step explanation:

15 inches is the width

The formula for density is given by p equals startfraction m over v endfraction, where p is density, m is mass and v is volume. if a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml? 7.7 7.7278 7.73 0.1

Answers

Answer:

it is 7.73

Step-by-step explanation:

Get smarter

Do subtraction

Answer:

The Answer is 7.73

Step-by-step explanation:

do some basic math lol

PLEASE HELP URGENTLY! RIGHT ANSWERS ONLY!

Answers

Answer:

Hi! The answer is B!

I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)

Identify the errors made in finding the inverse of
y = x2 + 12x.

An image shows a student's work. Line 1 is x = y squared + 12 x. Line 2 is y squared = x minus 12 x. Line 3 is y squared = negative 11 x. Line 4 is y = StartRoot negative 11 x EndRoot, for x greater-than-or-equal 0.
Describe the three errors.

Answers

The errors made by the student are:

The variables y and x are not properly swappedThe square root should include the ± signThe domain of the function is incorrect

How to identify the errors?

The equation is given as:

[tex]y = x^2 + 12x[/tex]

The first step of the student is given as:

[tex]x = y^2 + 12x[/tex]

This is incorrect because the variables x and y must be completely swapped.

So, the actual step is [tex]x = y^2 + 12y[/tex]

The second step is given as:

[tex]y^2 = x - 12x[/tex]

The third step is given as:

[tex]y^2 = - 11x[/tex]

The last step is given as:

[tex]y = \sqrt{-11x}[/tex] for [tex]x \ge 0[/tex]

This is incorrect because [tex]y = \sqrt{-11x}[/tex]  would have complex solution for [tex]x \ge 0[/tex] and the square root needs to have a ±

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