The Total solution for NCERT class 6-12
Let us consider LHS:
√[(1 – cos 2x) / (1 +cos 2x)]
We know that cos 2x = 1– 2 sin2 x
= 2 cos2 x – 1
So,
√[(1 – cos 2x) / (1 +cos 2x)] = √[(1 – (1 – 2sin2 x))/ (1 + (2cos2x – 1))]
= √[(1 – 1 + 2sin2 x) / (1 + 2cos2 x – 1)]
= √[2 sin2 x / 2 cos2 x]
= sin x/cos x
= tan x
= RHS
Hence proved.