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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
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.