Question

Prove the following trigonometric identities:

`((1 + sin theta)^2 + (1 - sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`

Answer 1

LHS = `(1 sin^2 theta + 2 sin theta + 1 + sin^2 theta -  2 sin theta)/(2 cos theta)`

`=> (2(1 + sin^2 theta))/(2 cos^2 theta) => (1 + sin^2 theta)/(1 - sin^2 theta)`     `[∵ cos^2 theta = 1 - sin^2 theta]`

∴ LHS = RHS Hence proved