(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

Jim donates 22% of his monthly salary to charity. If his monthly salary is $2257, approximately how much of his salary does Jim keep?

Answers

1760.46. 2257- 22% or 2257 * .22

Answer correctly and get brainless and 20 points

Answers

Answer:

D. x = 12.4

Step-by-step explanation:

A. (2.4) - 5 = 7.4

-2.6 = 7.4

B. (6.9) - 5 = 7.4

1.9 = 7.4

C. (7.9) - 5 = 7.4

2.9 = 7.4

D. (12.4) - 5 = 7.4

7.4 = 7.4

Please help me please pleaee

Answers

Hello,

A.i. the circumference of a circle is nothing else but its perimeter which formula is π × diameter = π × 2 × radius

Let π = 22/7 ≈ 3.142857, the egyptian approximation

Then if C is the circumference of the circle i., C = 22/7 × 21 = (22 × 21) / 7 = (22× 7×3 )/7 = 22 ×3 = 66 cm

ii. Applying the same formula for the second circle gives us C = 22/7 × 8 = 176/7 ≈ 25.14 meters, rounded to the nearest hundredth...

Good luck !

Answer:

a) 66cm.       b) 50.28cm. or 50 2/7cm.

Step-by-step explanation:

The circumference of a circle is C=2πr or C=πd.

π=22/7

a)  C=πd

Plugin the diameter.

C=22/7 x 21

=66cm.

b) C=2πr

Plugin the radius.

C=2 x 22/7 x 8

=50.28cm. or 50 2/7cm.

Hope this helps :)

PLSSS HELP!!!! I offer 25 points!!

A box has a volume of 1008 cubic inches. Your friend told you that he found the polynomial that represents the volume of the box: 4x³-28x² +144x. If x is the height of the box how tall is the box?

Answers

Answer:

  7 inches tall

Step-by-step explanation:

A graphing calculator quickly finds the solution to the cubic equation. It is convenient to define ...

  f(x) = 4x^3 -28x^2 +144x -1008

so f(x) = 0 gives the value of x that is of interest. That value is x=7.

The box is 7 inches tall.

_____

The equation f(x) = 0 can be divided by 4 to give ...

  x^3 -7x^2 +36x -252 = 0

This can be factored by grouping:

  (x^3 -7x^2) +(36x -252) = 0

  x^2(x -7) +36(x -7) = 0

  (x -7)(x^2 +36) = 0

The only real root is x = 7, which makes a factor zero.

_____

Additional comment

For finding solutions to cubic and higher-degree polynomials, I find a graphing calculator to be an extremely helpful tool. Desmos provides an online calculator and apps for various platforms. It may take a little while to learn how to use it effectively, but it can save immense amounts of time and frustration. Of course, your handheld graphing calculator can be just as useful.

Graph the line passing though (-6,-1) whose slope is m= -4/3

Answers

y=-4/3x-9

hope it helps

Hyung-Jin did an analysis of starting salaries of elementary school teachers in his area. He called three schools and was quoted the following salaries: \$28,300,\$27,000 , and $ 3,000, . What is the average salary in his area? Show your work.

Answers

Answer:

average - $19,333.33

Step-by-step explanation:

$28,300, $27,000 , and $ 3,000

total =58,000/3 = 19,333.33

How to find missing angle of a right triangle given 2 sides

Answers

Answer:

As a rule of thumb, if you know only the two shorter side, their ratio is the tangent of the angle opposed to the side you use as a numerator.

If you know one side and the hypotenuse, the ratio side/hypotenuse is either the sine of the opposite angle, or the cosine of the adjacent angle.

b. Solve 3v – 5 = 2v + 10 by gathering the constant terms on the left side
and the variable terms on the right side of the inequality.

Answers

Answer:

so subtract -2v to the left side add 5 to the right side so your left with

v = 15

Answer:

15 = v

Step-by-step explanation:

First start by grouping like terms,

=> - 5 - 10 = 2v - 3v

evaluate the LHS and RHS

=> - 15 = - v

Divide through by the coefficient of v, which in this case is - 1

=>

[tex] \frac{ - 15}{ - 1} = v[/tex]

Therefore, 15 = v

15.6 degrees Fahrenheit in 13 minutes

Answers

Answer:

1.2 degree Fahrenheit per minute.

per minute.

Step-by-step explanation:

We are supposed to find the unit rate for 15.6°F in 13 minutes.

To find the unit rate for our given scenario, we will divide 15.6 by 13 as:

Therefore, our required unit rate would be 1.2 degree Fahrenheit per minute.

PLEASE HELP GIVING BRAINLIEST :)

Answers

the answer to this is 3

1/6 to the power of 3

Answers

Answer:

0.00462962962

Step-by-step explanation:

Camilla thinks that -5 is less than -7 because 5 is smaller than 7.explain why Camilla is correct

Answers

Think of a vertical number line. The positive values count down as we move down this number line. The negative numbers count up, so to speak, as we move down the number line. So we have -1, -2, -3, ... as we move down. This indicates that -5 is not smaller than -7.

Diagram is below.

PLZ HELP ME with this hw

Answers

C because from the eqn :AB=AD=DC=BC so it is a parallelogram or a rhombus

7990 was rounded to the nearest ten. What is the lower bound?

Answers

Here we will tell you what 7990 is rounded to the nearest ten and also show you what rules we used to get to the answer.

Remember, we did not necessarily round up or down, but to the ten that is nearest to 7990.

First, 7990 rounded to the nearest ten is:

7990

Sophie can cut Two-fifths ft piece from a 4 ft length of wood.

Answers

Answer:

she can cut 2/20=18 left

Step-by-step explanation:

Answer:

the anser is 10 edge 2022

Step-by-step explanation:

which expression is equivalent to 3(x+5)-6
A) 3x-3
B)3x-1
C )3x+9
D) 15x-6

Answers

Answer:

answer C. 3x + 9

Step-by-step explanation:

3(x + 5) - 6 =

3x + 15 - 6 =

3x + (15 - 6 ) =

3x + 9

3(x+5)-6

Multiply 3 by the inside parenthesis:

3x+15-6

Subtract

3x+9

This means our answer is C) 3x+9

I hope this helps! :)

WILLL GIVE POINTS
Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of 1/3 and center of dilation at (0, 0) .
The points of the polygon =(3,3) (0,3) (6,-6) (9,6)

Answers

Answer:

(1,1) (0,1) (2,-2) (3,2)

Step-by-step explanation:

So with dilation you have to mulitply thE numbers by the one said in the problem which Was 1/3. So after doing that I got those coordinates.

HELP PLSASE: Find the solution of the system of equations.
2
x
+
4
y
=
2x+4y=



16
−16

2
x
+
2
y
=
−2x+2y=



2
−2

Answers

Answer:

Step-by-step explanation:

x

=

24

y

=

10

Explanation:

x

+

4

y

=

16

2

x

4

y

=

8

Subtract the bottom equation from the top one so the

+

4

y

and

4

y

cancel each other out.

x

=

24

x

=

24

x

+

4

y

=

16

24

+

4

y

=

16

4

y

=

40

y

=

10

Solve (x – 3)² =5 give your answers to the correct 3 significant figures

Answers

Answer:

5.236

Step-by-step explanation:

if the given data is 20,30 3x+5 divided by 2 ,50, 60 and the median is 40 find the value of x​

Answers

Answer:

in the image. Median is the middle number

Stacy and Jessica own a small business. Stacy, working alone can complete a job in 8 hours. Jessica can complete the same job in 9 hours. How long would it take them to complete the job working together?

Answers

Answer:

17 hour

Step-by-step explanation:

8+9=17

A coat is priced $50. If the sales tax is 7% of the price, how much is the sales tax? What is the total cost including sales tax?

Answers

Answer:

The sales tax is $3.5

The total cost is $53.5

Step-by-step explanation:

To find the sales tax, you have to find the 7 percent of 50 dollars. In decimal form, 7% is 0.07. So you just have to multiply 0.07 to 50.

50 x 0.07 = 3.5

That's why $3.5 is the sales tax.

In order to get the total cost including sales tax. You just have to add $50 to the sales tax which is $3.5.

$50 + $3.5 = $53.5

2H20 1) How many hydrogen atoms are represented by this much water? A) 1 B) 2 0.4 D) 6​

Answers

Answer is B)2
2 hydrogen atom in the water molecule
H2O

Which sentence in this conclusion paragraph most clearly reminds the reader of the main points?

(1) As the evidence has shown, Faith is not only Goodman Brown's wife but also a symbol of his weakening faith. (2) He ignores her advice not to leave Salem, and he loses her in the woods, two events that show that his faith is fading
(3) Indeed, the ending of the story suggests that his faith is never restored.(4) In many ways, Goodman Brown's relationship with faith and Faith is a warning.


(A. Sentence 1
( B. Sentence 4
( C. Sentence 2
( D. Sentence 3

No links.​

Answers

Answer:

Step-by-step explanation:

I’m doing this too right now and can’t figure it out

The answer is A. Sentence 1

Which of the fractions below is closest to zero? 1/4 1/5 1/6 1/8

Answers

Answer:

the answer to this question is 1/8

Step-by-step explanation:

1/4 is the biggest of the fractions,with 1/5 being the second biggest,and 1/6 being the 3rd biggest which leaves 1/8 as being the smallest and closest to 0

becouse it Was coll and Arm to Freizeit time

The perimeter of a rectangle is 40 cm. The length is 14 cm.
Let x = width of the rectangle.
Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.
Answer the questions to solve the equations and to compare the steps and solutions.
1. Which of these is the most helpful first step for solving Ravi's equation, 2(x + 14) = 40?
Circle the best answer.
Add 14 to both sides
Subtract 14 from both sides
Divide both sides by 2
Multiply both sides by 2














2. What would your next step be?

Write your answer in the space below.














3. Solve Ravi's equation, 2(x + 14) = 40, to find the width of the rectangle. Show your work.

Write your answer in the space below.2(x +14) = 40 (use the distributive property)
2x + 28 = 40 (solve exactly like you did for Fran)
2x = 12
x = 6















4. Which of these is the most helpful first step for solving Fran's equation, 2x + 28 = 40?
Circle the best answer.
Multiply both sides by 2
Subtract 28 from both sides
Divide both sides by 2
Add 28 to both sides














5. What would your next step be?

Write your answer in the space below.














6. Solve Fran's equation, 2x + 28 = 40, to find the width of the rectangle. Show your work.

Write your answer in the space below.














7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense.

Write your answer in the space below

Answers

Answer:

Below.

Step-by-step explanation:

1. Divide both sides by 2.

2. After dividing both sides by we would have:

x + 14 = 20

The next step would be

Subtract 14 from both sides.

3. 2(x + 14) = 40

x + 14 = 20

x = 20 - 14

x = 6.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6.

In two or more complete sentences, explain how to use ordered pairs of points in S (x) and g(z) to determine if (2)
and g(x) are inverses of each other

Answers

Answer:

x=2x4=s

Step-by-step explanation:

because x+2x4=s

help me with this please and thank you !!

Answers

Answer:

I hope this helps.

In addition to the car payment, Jackson and Bonnie estimate they will spend $200 on utilities, $140 on gasoline, $200 for groceries, $55 for cell phone, and $45 for car insurance. What will be the total of the monthly bills?

Answers

The total of the monthly bills will be $640.

(Add all of the bills together)
The answer is 640.


Explanation: if you add them all together you can get the answer.

Find the equation of this line. i’m really confused and i really need help.

Answers

Y=-2/5+1 ?I think this is right
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