Prove the trigonometric identity (tan(x)^2)/(1-sec(x)^2)=-1

 Exercise

$\frac{\left(tan^2\left(x\right)\right)}{1-sec^2\left(x\right)}=-1$

 

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

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

 

Apply the trigonometric identity: $-\sec\left(\theta \right)^2+1$$=-\tan\left(\theta \right)^2$

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

 

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

$-1$

 

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

true

true

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