A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$
Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$
$1-2\cos\left(x\right)\sin\left(x\right)$
Why is sin(x)^2 + cos(x)^2 = 1 ?
Final answer to the problem
$1-2\cos\left(x\right)\sin\left(x\right)$
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Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.