Question

Prove that : $b^2{x}^2-a^2{y}^2=a^2{b}^2$,

If: $x=acosec\theta ,y=b\cot \theta$

Answer 1

$\left(ii\right)x=a\csc \theta ,y=b\cot \theta$

By substituting the values of $x$ & $y$, we get

$b^2{x}^2-a^2{y}^2$

$=b^2(a\csc \theta {)}^2-a^2(b\cot \theta {)}^2$

$=a^2{b}^2({\csc }^2\theta -{\cot }^2\theta )$

$=a^2{b}^2\left(1\right)$, using Identity ${\csc }^2\theta -{\cot }^2\theta =1$

$=a^2{b}^2$

Hence Proved

$\left(i\right)$ Wrong Question