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=(1+\cos4x)/(8)`

Step-by-step explanation:

Given the expression:

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

This may be written as:

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