Prove that


To Prove:

Taking LHS,


= cos4x + sin4x


Adding and subtracting 2sin2x cos2x, we get


= cos4x + sin4x + 2sin2x cos2x – 2sin2x cos2x


We know that,


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


= (cos2x + sin2x) – 2sin2x cos2x


= (1) – 2sin2x cos2x [∵ cos2 θ + sin2 θ = 1]


= 1 – 2sin2x cos2x


Multiply and divide by 2, we get





[∵ sin 2x = 2 sinx cosx]



= RHS


∴ LHS = RHS


Hence Proved


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