(sinx + cosx)(1 − sinx cosx) ≡ sin3x + cos3x

Answers

Answer 1

Step-by-step explanation:

We will use the LHS to find the RHS.

Step 1: Expand the LHS by multiplying through the brackets and simplify

(sinx + cosx)(1 − sinx cosx) ≡  sinx + cosx - (sinx + cosx (sinx cosx))

                                             ≡  sinx + cosx - sin²x cosx - sinx cos²x

Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation

                                           ≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)

Step 3: Simplify the equation by adding like terms

                                           ≡ sinx + cosx - cosx + cos³x - sinx + sin³x

                                           ≡ sin³x + cos³x                 [QED]

Reminder:

1 - cos²x = sin²x  1 - sin²x = cos²x (cosx)(cosx) = cos²x


Related Questions

the equation p=2l+20 gives the perimeter P (in inches) of a rectangular box with a length of l feet. Identify the independent and dependent variables.

Answers

Length is the independent variable while P is the dependent variable.

The dependent and independent variable

Independent variables are variables that can stand alone while dependent are depend on others.

Independent variables are input variables of a function whole independent are the output variables of a function.


Given the function as shown:

P = 2l + 20

length is the independent variable while P is the dependentw variable.

Learn more on independent and dependent variables here; https://brainly.com/question/25223322

please help me answer this question​

Answers

1) The mathematical statements in Set A are linear equations (there's the equal to [=] symbol). The mathematical statements in Set B are linear inequalities (there are inequality signs like <, > etc).

2) Set A (=)

3) Set B (<, > etc.)

_______

Hope it helps ⚜ :))

X+3y=24

Please solve super fast

Answers

Step-by-step explanation:

x+3y=24

3y/3=24/3

x+y=8

divide x to both side not to y

y=-x +8

There are 30 coins in 5 rows.

How many coins in each row?

Answers

Answer:

It is 30 divide by 5

Step-by-step explanation:

URGENT!!!

Peggy sue decided to enter her famous “Five- Alarm chili” at her local chili cooking contest. Normally, she needs 5 tomatoes to make enough chili for her family of 7

A. How many tomatoes should she expect to use to make her famous recipe for 100 people?

b. When she gets to the contest, she realizes that she only packed 58 tomatoes. How many people can she expect to feed?

Answers

A. If she needs 5 tomatoes for a family of seven, then we need to find how many tomatoes it takes to feed only one person and then multiply that by 100z

5/7 = 0.714… tomatoes per person

Multiply this by one hundred

0.714 * 100 = 71.43 tomatoes.

Check:

5/7 = ?/100

Solve for ?

? = 71.43 tomatoes, but you technically can’t bring 0.43 tomatoes, so round that to 72 tomatoes

B. We would need to solve for

5/7 = 58/?

? = 81.2 people, but you should round down here because there isn’t enough chili for that 82 person, and there are not 20% of a person walking around looking for some chili.

Mark of Ben in semester 1 examination is 586:600. Convert it into percentage

Answers

Answer:

97.67

Step-by-step explanation:

600 = 100%

586 = x%

[tex]\frac{100}{x} = \frac{600}{586}[/tex]

x = [tex]\frac{586.100}{600}[/tex] = [tex]\frac{586.100}{6.100}[/tex] = [tex]\frac{586}{6}[/tex] = 97.67

PLEASE HELP I need the answer please ​

Answers

17. <

18.=

19.>

20.>

21.3.021,3.12,3.121,3.21

22. 1.03,1.03,1.3,1.39

23.

I really need help with this and happy thanksgiving

Answers

Answer:

C (-2,2)

D (1,-2)

Step-by-step explanation:

happy thanksgiving!

-5(2x -3) + 4x = - 3x + 6

Answers

We have -5(2x-3) + 4x = -3x + 6
<=> -10x + 15 + 4x = -3x + 6
<=> -10x + 4x + 3x = 6 - 15
<=> -3x = -9
<=> x = 3

Ok done. Thank to me:>

4. Aidan wrote the interval (-5, 4) and claimed it was equivalent to the graph below. Explain what he did
wrong and correct his mistake.

Answers

Please attach the graph so I can help you. :)

Write the slope-intercept form for the line with a slope of 2 and a y-intercept of 12.


Answers

Answer:

y = 2x + 12

Step-by-step explanation:

In a Quiz points are rewarded for each correct answer while points are deducted for each incorrect answer. In the first round, Ethan answered all the questions correctly. In the second round, he answered 8 questions incorrectly. If 3 points are deducted for each incorrect answer, by how much does Ethan’s score change in the second round?

Answers

Answer:

24 points

Step-by-step explanation:

3x8 is 24


Write a converse theorem that proves lines a and b below are parallel.
If _______ _______ angles are ________, then two lines vk it by a transversal are parallel.

Answers

Taking into account the definition of corresponding angles and Corresponding Angles Theorem, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.

First of all, remember that a transverse line is a line that crosses or passes through two other lines. Sometimes the other two lines are parallel and the transversal passes through both lines at the same angle. However, the other two lines do not have to be parallel for a transversal to cross them.

Corresponding angles

Corresponding angles are angles formed when a transverse line crosses two straight lines. These angles are formed at equivalent corners or at corners corresponding to the transversal when two lines are intersected by a third line.

In other words, if a transversal line intersects two parallel lines, the corresponding angles are those that are on the same side of the parallels and on the same side of the transversal.

Corresponding Angles Theorem

The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then the corresponding pairs of angles are congruent.

Remember that if two angles are congruent, then they have the same measure.

The opposite of this theorem is also true:  If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

In summary

In summary, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.

Learn more about corresponding angles theorem:

https://brainly.com/question/12122049?referrer=searchResultshttps://brainly.com/question/18250950?referrer=searchResultshttps://brainly.com/question/12101094

What is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y-3= (x+4)
y–4= (x+3)
y+4= (x+3)
y+4= (x+3)​

Answers

Point-Slope Form: y + 1 = - 5/7 • ( x - 4 ). Slope intercept form: y = -5/7 + 13/7. The choices you have are incorrect

6 of 15 motorist is what percent

Answers

Answer:

40%

Step-by-step explanation:

6/15 is the same as 2/5 which is .40 or 40%

Answer:

40%

Step-by-step explanation:

Which student used the correct steps to construct rhombus PQRS?

Answers

Answer:

  Student 1

Step-by-step explanation:

In order to accomplish the next step of construction PS║QR, the angle LQM must be copied to make angle NPT. That is done by drawing arc NT (centered at P) so it has the same (chord) length as arc LM.

This step is only accomplished by Student 1.

Find the equation of the line perpendicular to the given line and passing through the given point.

y = -4x + 2;(-1,4)

Answers

Step-by-step explanation:

hope it helps you.......

Here is your answer refer to the attachment .

Look at the screen shot and answer the question. Please Explain !!

Answers

Answer:

see explanation

Step-by-step explanation:

- 4x + 3 < 23 ( subtract 3 from both sides )

- 4x < 20

x < - 5 ← Her error is on this step

When dividing by a negative quantity the symbol is reversed, that is

Divide both sides by - 4 and reversing the symbol gives

x > - 5

please help me with this

Answers

The answer is 6 units. The reason for this is in order to find the volume you need to calculate base times height. In this case the base is 4 1/2 and the height is 1 1/3. First turn the fraction like so… 9/2 x 4/3 = 36/6 than 36/6 divided by6 = 6 . Hope that helps

PLEASE HELP WILL MARK BRAINILEST

1. The formula for the volume of a rectangular box is V = lbh. What is the formula for h in terms of V, l and b?

2. Solve 7x + 3y = m, for y

3.The formula for the potential energy P = mgh. What is the formula for m in terms of P, g, and h?

Answers

Answer:

1. h = V/lb

2. y = (m - 7x)/3

3. m = P/gh

can some one help me

Answers

Answer:

y=x-3

Hope This Helps!!!

sorry here is the question!! please help and Thank you!!

Answers

Answer:

B.   4

Step-by-step explanation:

[tex] \dfrac{\sqrt{32}}{\sqrt{2}} = [/tex]

[tex] = \dfrac{\sqrt{16 \times 2}}{\sqrt{2}} [/tex]

[tex] = \dfrac{\sqrt{16} \times \sqrt{2}}{\sqrt{2}} [/tex]

[tex] = \dfrac{4\sqrt{2}}{\sqrt{2}} [/tex]

[tex] = 4[/tex]

Please help me. I'm struggling with my math

Answers

Answer:

a. (4, -3)

b. (-2.5, -4)

Step-by-step explanation:

a. 2x - 4y = 20

x = 4

step 1: plug in x value

2(4) - 4y = 20

8 - 4y = 20

Subtract 8 on both sides

-4y = 12

divide both sides by -4

y = -3

b. y = 6x + 11

2x - 3y = 7

step 1: plug in the y value

2x - 3(6x + 11) = 7

step 2: distribute

2x - 18x  - 33 = 7

add 33 from both sides and combine like terms

-16x = 40

divide both sides by -16

x = -2.5

Okay now you plug in the x value to solve for y

y = 6(-2.5) + 11

y =-4

Two legs of a right triangle are each 70 cm. If one leg grows at the rate of 3cm/min and the other
shrinks at the rate of 5 cm/min.
B)How fast is the area of the triangle changing 2 minutes later?

Answers

Answer: 5 in

Step-by-step explanation: Consider a right triangle which is changing shape in the following way. The horizontal leg is increasing at the rate of 5 in.

Create a shape with an area of 0.8 m2 and a perimeter close to 400 cm

Answers

The dimension of the shape is approximately 1.45 meters by 0.55 meters

Assume the shape is a rectangle, that has the following dimensions.

Length = x

Width = y

So, the area is:

Area = xy

The perimeter is

Perimeter = 2(x + y)

Substitute known values

[tex]\mathbf{xy = 0.8m^2}[/tex]

[tex]\mathbf{2(x+y) = 400cm}[/tex]

Express cm as m

[tex]\mathbf{2(x+y) = 4m}[/tex]

Divide through by 2

[tex]\mathbf{x+y = 2m}[/tex]

Make x the subject (ignore the units)

[tex]\mathbf{x= 2 - y}[/tex]

Substitute 2-y for x in [tex]\mathbf{xy = 0.8m^2}[/tex]

[tex]\mathbf{(2-y)y = 0.8}[/tex]

Open brackets

[tex]\mathbf{2y-y^2 = 0.8}[/tex]

Rewrite as:

[tex]\mathbf{y^2 - 2y + 0.8 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{y \approx (0.55,1.45)}[/tex]

Recall that:

[tex]\mathbf{x= 2 - y}[/tex]

So, we have:

[tex]\mathbf{x \approx (2-0.55,2-1.45)}[/tex]

[tex]\mathbf{x \approx (1.45,0.55)}[/tex]

Hence, the dimension of the shape is approximately 1.45 meters by 0.55 meters

Read more about areas and perimeters at:

https://brainly.com/question/11957651

-6x + 8y = 12 and -3x + 4y = 6

Answers

Answer:

y = (3/4)x + (3/2)

Step-by-step explanation:

all points on that line

hey can someone help with my assignment worth 80% of my grades

Answers

Answer:

Honestly the intercept should be on the axis

Step-by-step explanation:

Answer:

You didn't helped me with my question so no

Step-by-step explanation:

Help please :) I’m quite stuck on this one

Answers

Answer:

-4-4i

That's the answer for the question

help please i only have 10 mins left

Answers

Answer:

d.

took the test

Step-by-step explanation:

Solve for x. Round to the nearest tenth, if necessary. S 210 X 5.5​

Answers

Answer:

1155.0

Step-by-step explanation:

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