Prove the Identity sin5x 18sinx 3 4cos2x cos4xSolutionsin

Prove the Identity: sin⁵x = (1/8sinx)( 3 - 4cos2x + cos4x)

sin⁵x = (1/8sinx)( 3 - 4cos2x + cos4x)

sin⁵x = (1/8sinx)( 3 - 4(1-2sin^2x) + (1- 2sin^2(2x)))

sin⁵x = (1/8sinx)( 3 - 4 - 8sin^2x) + 1- 2sin^2(2x))

sin⁵x = (1/8sinx)( 3 - 4 - 8sin^2(x) + 1- 2(2sinx cos x)^2)

sin⁵x = (1/8sinx)( - 8sin^2(x) - 8 sin^2(x) cos ^2(x))

sin⁵x = (1/8sinx)( - 8sin^2(x) - 8 sin^2(x) (1 - sin ^2(x)))

sin⁵x = (1/8)sin(x)(8sin^2(x) - 8sin^2(x) + 8sin^4(x))

sin⁵x = (1/8)sin(x)( 8sin^4(x))

sin⁵x = sin⁵x