Prove the trigonometric identity (cos(x)^2)/(1-cos(x)^2)=cot(x)^2

 Exercise

$\frac{cos^2\left(x\right)}{1-cos^2\left(x\right)}=cot^2\left(x\right)$

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Starting from the left-hand side (LHS) of the identity

$\frac{\cos\left(x\right)^2}{1-\cos\left(x\right)^2}$

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

$\frac{\cos\left(x\right)^2}{\sin\left(x\right)^2}$

 Why is 1 - cos(x)^2 = sin(x)^2 ?

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Applying the cotangent identity: $\displaystyle\cot\left(\theta\right)=\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}$

$\cot\left(x\right)^2$

 

Since we have reached the expression of our goal, we have proven the identity

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