Question

Prove (1+cos 2x )/sin 2x = cot x

Answer 1

1+cos2x=2cos²x......(1)

sin2x=2sinxcosx......(2)

equation (1) divide equation (2)

(1+cos2x)/sin2x = 2cos²x/2sinxcosx

=cosx/sinx

=cot x

Answer 2

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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