Question

Evaluate: sin π/ 4 cos π/12 +cos π/4 sin π/12

Answer 1

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answer..

Let us consider the LHS cos2 π/4 – sin2 π/12 As we know that, cos2A – sin2 B = cos (A + B) cos (A – B) Therefore, cos2 π/4 – sin2 π/12 = cos(π/4 + π/12) cos(π/4 – π/12) = cos 4π/12 cos 2π/12 = cos π/3 cos π/6 = 1/2 × √3/2 = √3/4 = RHS ∴ LHS = RHS Thus proved.

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