Question

Prove that 1-cosx/sinx = tan x/2 = sinx/1+cosx

Answer 1

Step-by-step explanation:

wkt Sin x = 2 sin x/2 cos x/2

1 + cos x = 2 Cos ^2( x/2)

1- Cos x = 2 Sin ^2(x/2)

substitute those in given equation and compare

given 1-cosx /sinx= tan x/2 = sinx / 1+ cosx

2 sin ^2(x/2) / 2 sin x/2 cos x/2 = tan x/2 = 2sin x/2 cos x/2 / 2 cos^2(x/2)

cancle the common terms in numerator and denominator then we get

sin x/2 / cos x/2 = tan x/2 = sin x/2 / cos x/2

wkt sin x/2 / cos x/2 = tan x/2

tan x/2 = tan x/2 = tan x /2