Sin 6x+sin2x=2 sin4x Cos 2x
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Answer:
Use : sin(A+B) = sinAcosB + cosA.sinA
sin2θ = 2sinθcosθ
cos2θ = 2cos²θ -1
Step-by-step explanation:
LHS = sin6x + sin2x
= sin(4x + 2x) + sin2x
= sin4x cos2x + cos4x sin2x + sin2x
= 2sin2x.cos2x cos2x + cos4xsin2x + sin2x
= sin2x [2cos²2x + cos4x +1]
= sin2x [ 2cos²2x + 2cos²2x -1 +1]
= sin2x [4 cos²2x]
= 2 [2sin2xcos2x] cos2x
= 2 sin4x cos2x
= RHS
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