Expand and simplify the trigonometric expression cot(a)^2(tan(a)^2-sin(a)^2)

 Exercise

$\cot\left(a\right)^2\left(\tan\left(a\right)^2-\sin\left(a\right)^2\right)$

 

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

$\tan\left(a\right)^2\cot\left(a\right)^2-\sin\left(a\right)^2\cot\left(a\right)^2$

 

Applying the trigonometric identity: $\tan\left(\theta\right)\cdot\cot\left(\theta\right)=1$

$1-\sin\left(a\right)^2\cot\left(a\right)^2$

 

Use trig identities to simplify $-\sin\left(a\right)^2\cot\left(a\right)^2$ in terms of $\cos$

$1-\cos\left(a\right)^2$

 

Applying the trigonometric identity: $1-\cos\left(\theta \right)^2 = \sin\left(\theta \right)^2$

$\sin\left(a\right)^2$

 Why is 1 - cos(x)^2 = sin(x)^2 ?

$\sin\left(a\right)^2$

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