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hichkok12 [17]
3 years ago
10

Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

Mathematics
1 answer:
otez555 [7]3 years ago
4 0

<u>Step-by-step explanation:</u>

To prove:

\cos 3x=\cos^3x-3\sin^2 x\cos x

Identities used:

\cos(A+B)=\cos A\cos B+\sin A\sin B      ......(1)

\sin 2A=2\sin A\cos A        ........(2)

\cos 2A=\cos^2A-\sin^2 A     .......(3)

Taking the LHS:

\Rightarrow \cos 3x=\cos (x+2x)

Using identity 1:

\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x

Using identities 2 and 3:

\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x

As, LHS = RHS

Hence proved

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The squares are identical. What is the area of each square?
Nastasia [14]

Answer:

A = 256 units^2

Step-by-step explanation:

If the squares are identical, then the side lengths are identical

3x+7 = 5x+1

Subtract 3x from each side

3x+7-3x = 5x-3x+1

7 = 2x+1

Subtract 1

7-1 =2x+1-1

6 = 2x

Divide by 2

6/2 =2x/2

3 =x

The side length is 3x+7 = 3*3 +7 = 9+7 = 16

The area is

A = s^2 where s is the side length

A = 16^2

A = 256 units^2

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Good morning ☕️

____________________

Step-by-step explanation:

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Jasmine earns $1200 per month as a base salary, plus 3% of her total sales. Write a linear model of her monthly earnings. Then u
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Answer:

The linear model of her monthly earnings is; Y =1200 +0.03*X. The amount earned is 1350; choice A

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