Question

Hi this is part of my homework I'm struggling with so, if possible, 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 one.

Answer 1

Answer:$\sin ^2x\cos ^2x=\frac{1+\cos4x}{8}$

Explanation:

Given the expression:

$\sin ^2x\cos ^2x$

This may be written as:

$\begin{gathered} \sin ^2x\cos ^2x \\ =(\frac{1-\cos2x}{2})(\frac{1+\cos 2x}{2}) \\ \\ =(\frac{1}{4})(1-\cos ^22x) \\ \\ =\frac{1}{4}(\frac{1+\cos 4x}{2}) \\ \\ =\frac{1+\cos 4x}{8} \end{gathered}$