Question

if sec theta + tan theta=x then prove that sin theta=x^2-1/x^2+1

Answer 1

hope it helps you..

Answer 2

Answer:

$Given \: sec\theta + tan\theta = x---(1)$

$Now, RHS =\frac{x^{2}-1}{x^{2}+1}$

$= \frac{(sec\theta+tan\theta)^{2}-1}{(sec\theta+tan\theta)^{2}+1}$

$=\frac{sec^{2}\theta+tan^{2}\theta+2sec\theta tan\theta-1}{sec^{2}\theta+tan^{2}\theta+2sec\theta tan\theta+1}$

$=\frac{(sec^{2}\theta-1)+tan^{2}\theta+2sec\theta tan\theta}{sec^{2}\theta+sec^{2}\theta-1+2sec\theta tan\theta+1}$

$=\frac{tan^{2}\theta+tan^{2}\theta+2sec\theta tan\theta}{2sec^{2}\theta+2sec\theta tan\theta}$

$=\frac{2tan^{2}\theta+2sec\theta tan\theta }{2sec\theta(sec\theta+tan\theta}$

$=\frac{2tan\theta(sec\theta+tan\theta)}{2sec\theta(sec\theta+tan\theta)}$

$=\frac{tan\theta}{sec\theta}$

$=\frac{\frac{sin\theta}{cos\theta}}{\frac{1}{cos\theta}}$

$=sin\theta$

$= LHS$

•••♪