Question

Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.sin2(3x) cos2(3x)

Answer 1

The expression
`\sin^2(3x)\cos^2(3x)` in terms of cosines is
`\cos^2(3x) - \cos^4(3x)`

How to rewrite the expression in terms of cosines

From the question, we have the following parameters that can be used in our computation:

`\sin^2(3x)\cos^2(3x)`

The sin and cosine identity represented as

`\sin^2(x) + \cos^2(x) = 1`

So, we have

`\sin^2(3x)\cos^2(3x) = [1 - \cos^2(3x)]\cos^2(3x)`

Expand the equation

`\sin^2(3x)\cos^2(3x) = \cos^2(3x) - \cos^4(3x)`

Hence, the expression in terms of cosines is
`\cos^2(3x) - \cos^4(3x)`

Answer 2

Step-by-step explanation:

Here, we want to use the power-reducing formula

We have that as follows:

`\begin{gathered} sin^2(3x)cos^2(3x)\text{ = } \\ sin^2\text{ 3x = }\frac{1-cos\text{ 6x}}{2} \\ \\ cos^23x\text{ = }\frac{1+cos\text{ 6x}}{2} \end{gathered}`

Thus, we have the product as: