यदि `sec theta+tan theta=p,` हो,तो सिद्ध करो कि `(p^(2)-1)/(p^(2)+1)=sin theta`

Explanation

`LHS=(p^(2)-1)/(p^(2)+1)=((sec theta+ tan theta)^(2)-1)/((sec theta + tan theta)^(2)+1)`
`impliesLHS =(sec ^(2)theta + tan ^(2)theta+ 2 sec theta tan theta-1)/(sec ^(2)theta + tan ^(2)theta+2 sec theta tan theta+1)`
`impliesLHS=((sec ^(2)theta-1)+tan ^(2)theta+2 sec theta tan theta)/(sec ^(2)theta+2 sec thetatan theta+ (1+tan ^(2)theta))`
`impliesLHS =(tan ^(2)theta + tan ^(2)theta+2 sec thetatan theta)/(sec ^(2)theta+2 sec thetatan theta+sec ^(2)theta)`
`impliesLHS (2 tan ^(2)theta+2tan theta sec theta)/(2 sec^(2) theta +2 sec theta tan theta)`
`impliesLHS =(2 tan theta (tan theta + sec theta))/(2 sec theta(sec theta+tan theta))`
`implies LHS=(tan theta)/(sec theta)=(sin theta)/(cos theta. sec theta)=sin theta=RHS`