1.

Prove the identity:√[(1 – cos 2x)/(1 + cos 2x)] = tan x

Answer»

Let us consider the LHS

√[(1 – cos 2x)/(1 + cos 2x)]

As we know that cos 2x = 1 – 2 sin2 x

= 2 cos2 x – 1

Therefore,

√[(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

Thus proved.



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