# Prove the followi

To prove: cot2 x – tan2 x = 4 cot 2x cosec 2x

Proof:

Take LHS:

cot2 x – tan2 x

Identities used:

a2 – b2 = (a – b)(a + b)

Therefore,

= (cot x – tan x)(cot x + tan x)

{ cot2 x + 1 = cosec2 x}

{ sin 2x = 2 sin x cos x}

= 4 cot 2x cosec 2x

= RHS

Hence Proved

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