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

 Exercise

$\frac{csc^2x-1}{cot^2x}=1$

 

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

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

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

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

 

Simplify the fraction $\frac{\cot\left(x\right)^2}{\cot\left(x\right)^2}$ by $\cot\left(x\right)^2$

$1$

 

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

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