Prove the following identities:


Proof:


Take LHS:



Identities used:




Therefore,






{∵ (a – b)(a + b) = a2 – b2;


(a + b)2 = a2 + b2 + 2ab &


(a – b)2 = a2 + b2 – 2ab}









{∵ cos2 x + sin2 x = 1 & cos 2x = cos2 x – sin2 x}




= 2 sec 2x



= RHS


Hence Proved


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