If $tan theta + sec theta=x$ ,then prove that $sin theta =(x^2-1)/(x^2+1)$ ?

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Answer 1 · 2017-08-14T15:15:47

If $tan theta + sec theta=x$ ,then prove that $sin theta =(x^2-1)/(x^2+1)$

Given
$tan theta + sec theta=x.....[1]$

$=>1/(sectheta+tantheta)=1/x$

$=>(sectheta-tantheta)/(sec^2theta-tan^2theta)=1/x$

$=>sectheta-tantheta=1/x....[2]$

Adding [1] and [2] we get

$2sectheta=x+1/x....[3]$

Subtracting [2] from [1] we get

$2tantheta=x-1/x....[4]$

Dividing [4] by [3] we get

$tantheta/sectheta=(x-1/x)/(x+1/x)$

$=>sintheta=(x^2-1)/(x^2+1)$

If tan theta + sec theta=x tan theta + sec theta=x,then prove that sin theta =(x^2-1)/(x^2+1) sin theta =(x^2-1)/(x^2+1) ?