Question

Sin 6x+sin2x=2 sin4x Cos 2x

Answer 1

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