Expand and simplify the trigonometric expression sin(t)^2(1-cot(t)^2)

 Exercise

$\sen^{2}\theta\left(1-\cot^{2}\theta\right)$

 

Multiply the single term $\sin\left(\theta\right)^2$ by each term of the polynomial $\left(1-\cot\left(\theta\right)^2\right)$

$\sin\left(\theta\right)^2-\cot\left(\theta\right)^2\sin\left(\theta\right)^2$

 

Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

$\sin\left(\theta\right)^2+\frac{-\cos\left(\theta\right)^2}{\sin\left(\theta\right)^2}\sin\left(\theta\right)^2$

 Why is cot(x) = cos(x)/sin(x) ?

 

Multiplying the fraction by $\sin\left(\theta\right)^2$

$\sin\left(\theta\right)^2-\cos\left(\theta\right)^2$

 

Applying the trigonometric identity: $\sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right)$

$-\cos\left(2\theta\right)$

 Why is cos(2x) = cos(x)^2 - sin(x)^2 ?

$-\cos\left(2\theta\right)$

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