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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.

Hi this is part of my homework I'm struggling with so, if possible, please show me-example-1
User Toashd
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1 Answer

23 votes
23 votes
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}

User Andrey Nikishaev
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