Question

Prove that sin theta -cos theta/sin theta+cos theta + sin theta +cos theta/sin theta-cos theta=2/2sin square theta+1

Answer 1

I think your question is incorrect at last it should be 2/ 2sin square theta -1
For simplicity I will take theta as x
Now
sin x - cos x/ sin x + cos x + sin x + cos x / sin x - cos x
Now take LCM
(sin x - cos x)^2 + (sin x + cos x)^2/ (sin^2 x - cos ^2 x)
Now expand
sin^2 x +cos ^2 x + sin^2 x + cos^2 x/ sin^2 x - cos^2 x as ( -2sinxcosx and 2sinxcosx are cancel out)

1 +1/ sin^2 x - cos^2 x
2/sin^2 x - (1 - sin^2 x) using sin^2 x + cos^2x=1
2/2sin^2 x -1
hence proved
Please mark it as brainliest If you think so...!!!