Question

(1+cosA/sinA)2 = 1+cosA/1-cosA​

Answer 1

Step-by-step explanation:

{(1-cosA+sinA)/(1+cosA+sinA)}^2= (1-cosA)/(1+cosA)

L.H.S.

={(1-cosA)+sinA}^2/{(1+cosA)+sinA}^2.

={(1-cosA)^2+sin^2A+2.(1-cosA).sinA}/{(1+cosA)^2+sin^2A+2.(1+cosA).sinA}.

={1–2.cosA+cos^2A+sin^2A+2.(1-cosA).sinA}/{1+2.cosA+cos^2A+sin^2A+2.

(1+cosA).sinA}.

={2(1-cosA)+2.(1-cosA).sinA}/{2(1+cosA)+2.(1+cosA).sinA}

= 2.(1-cosA).(1+sinA)/2.(1+cosA).(1+sinA).

= (1-cosA)/(1+cosA). Proved.