Answer :

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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