1 Answer

Import Random · Answer 1 · 2021-03-21T02:50:12+0000

Answer:

A

Explanation:

First, let's do the difference of two squares:

$(1-cos^4(\theta))=(1-cos^2(\theta))(1+cos^2(\theta))$

Note that
$sin^2(\theta)=1-cos^2(\theta)$ (Pythagorean Identity)

Thus, we can substitute:

$sin^2(\theta)(1+cos^2(\theta))$

Now, and I'm serious, you just have to use your creativity. After a while, you will find that:

$sin^2(\theta)+cos^2(\theta)=1$

So:

$1+sin^2(\theta)+cos^2(\theta)=1+1$

Thus, we have
$1+cos^2(\theta)=2-sin^2(\theta)$

Now, we can substitute:

$sin^2(\theta)(2-sin^2(\theta))=2sin^2(\theta)-sin^4(\theta)$

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