Question

(sec square theta - 1) ( cosec square Theta -1) = 1

Answer 1

using sec square x-tan square x=1 and cosec square x-cot square x=1

Answer 2

Answer and explanation:

To prove : $(\sec^2\theta -1)(\csc^2\theta-1)=1$

Proof :

Taking LHS,

$LHS=(\sec^2\theta -1)(\csc^2\theta-1)$

Using Trigonometric identity,

$\sec^2\theta -1=\tan^2\theta$

$\csc^2\theta -1=\cot^2\theta$

$LHS=(\tan^2\theta)(\cot^2\theta)$

We know, $\cot^2\theta=\frac{1}{\tan^2\theta}$

$LHS=\tan^2\theta\times \frac{1}{\tan^2\theta}$

$LHS=1$

$LHS=RHS$

Hence proved.