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Question -

sin 2x / (1 – cos 2x) = cot x



Answer -

Let us consider LHS:

sin 2x / (1 – cos 2x)

We know that cos 2x = 1– 2 sin2 x

Sin 2x = 2 sin x cos x

So,

sin 2x / (1 – cos 2x) =(2 sin x cos x) / (1 – (1 – 2sin2 x))

= (2 sin x cos x) / (1 –1 + 2sin2 x)]

= [2 sin x cos x / 2 sin2 x]

= cos x/sin x

= cot x

= RHS

Hence proved.

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