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opus

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## Homework Statement

Use the power reducing formulas to rewrite the expression that does not contain trigonometric functions of power greater than 1.

Given expression:

##4sin^2xcos^2x##

2. Homework Equations

2. Homework Equations

Relevant Power-Reducing Formulas:

##sin^2x=\frac{1-cos2x}{2}##

##cos^2x=\frac{1+cos2x}{2}##

## The Attempt at a Solution

$$4sin^2xcos^2x$$

$$=4\left(\frac{1-cos2x}{2}\right)\left(\frac{1+cos2x}{2}\right)$$

$$=4\left(\frac{1+cos2x-cos2x-cos^22x}{2}\right)$$

$$=4\left(\frac{1-cos^22x}{2}\right)$$

$$=2-cos^22x$$

The answer given is:

##\frac{1-cos4x}{2}##

Have I solved done a miscalculation somewhere, or is my entire approach to solving this wrong?

Thank you for any responses.