Question

please show me how to use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1 if you can, I have the steps already but I'm struggling to understand still.

Answer 1

Power reduction formulas for squares:

`\begin{gathered} \sin ^2u=(1-\cos (2u))/(2) \\ \\ \cos ^2u=(1+\cos (2u))/(2) \end{gathered}`

Given expression:

`72\sin ^2x\cos ^2x`

Use the reduction formula: For the given expression u is x:

`=72\cdot(1-\cos2x)/(2)\cdot(1+\cos2x)/(2)`

Simplify:

-Multiply:

`=(72\cdot(1-\cos 2x)(1+\cos 2x))/(4)`

-Divide 72 into 4:

`=18(1-\cos 2x)(1+\cos 2x)`

Then, an equivalent expression that does not contain powers of trigonometric functions greater than 1 is:

`18(1-\cos 2x)(x+\cos 2x)`