Question

Rewrite $sin^25xcos^25x$ simplified using power reduced formulas

Answer 1

Step-by-step explanation:

The power reducing formulas are given by the following:

$\sin^2 x = \dfrac{1- \cos2x}{2}$

$\cos^2 x = \dfrac{1+ \cos2x}{2}$

We can then write the given expression as

$\sin^25x \cos^25x$

$= \left(\dfrac{1- \cos 2(5x)}{2} \right) \left(\dfrac{1+ \cos 2(5x)}{2} \right)$

$= \dfrac{1}{4}(1- \cos 10x)(1+ \cos 10x)$

$= \dfrac{1}{4}(1- \cos^2 10x)$

$= \dfrac{1}{4} \left(\dfrac{1- \cos 20x}{2} \right)$

or

$\sin^25x \cos^25x= \dfrac{1}{8}(1- \cos 20x)$