Question

1+sinx+cosx/1+sinx-cosx=1+cosx/sinx help pls by proving

Answer 1

Below.

Explanation:

I'll write sin x as s and cos x as c so we have:

(1 + s +c)/(1 + s - c) = (1 + c)/s

Cross multiplying:

s + s^2 + cs = 1 + s - c + c + cs - c^2

s + s^2 + cs = 1 + s + cs - c^2

s^2 + c^2 + s - s + cs - cs = 1

s^2 + c^2 = 1.

- that is sin^2 x + cos^2 x = 1 which is a known identity.

Therefore the original identity is proved.