Final answer to the problem
$1+\sin\left(a\right)^2\left(-1+\cos\left(a\right)\right)$
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Step-by-step Solution
Specify the solving method
1
Applying the pythagorean identity: $\cos^2(\theta)=1-\sin(\theta)^2$
$1-\sin\left(a\right)^2+\sin\left(a\right)^2\cos\left(a\right)$
Why is 1 - sin(x)^2 = cos(x)^2 ?
2
Factoring by $\sin\left(a\right)^2$
$1+\sin\left(a\right)^2\left(-1+\cos\left(a\right)\right)$
Final answer to the problem
$1+\sin\left(a\right)^2\left(-1+\cos\left(a\right)\right)$