Question

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

Answer 1

L.H.S = (Sin + Cos) / (Sin - Cos) + (Sin - Cos) / (Sin + Cos)

By cross multiplication ,

= { (Sinx + Cosx)2 + (Sinx - Cosx)2 } / (Sin2x- Cos2x)

= { (Sin2x + Cos2x + 2 Sinx Cosx) + (Sin2x + Cos2x - 2 Sin Cosx) } / { Sin2x + Sin2x-1}

Canceling 2Sinx Cosx and -2Sinx Cosx and using the identity Sin2x + Cos2x = 1

= (1 + 1) / (2 Sin2x-1)