Dokazati da 32sin ^ 4x.cos ^ 2x = cos6x-2cos4x-cos 2x + 2?

# RHS = cos6x-2cos4x-cos2x + 2 #

# = Cos6x-cos2x + 2 (1 cos4x) #

# = - 2sin ((6x + 2x) / 2) * sin ((6x-2 x) / 2) + 2 * 2sin ^ 2 (2 x) *

# = 4sin ^ 2 (2 x) * -2sin4x sin2x = 4sin ^ 2 (2 x) -2 * 2 * * sin2x cos2x * sin2x #

# = 4sin ^ 2 (2 x) -4sin ^ 2 (2 x) * # cos2x

# = 4sin ^ 2 (2 x) 1-cos2x #

# = 4 x (2sinx * cosx) ^ 2 * ^ 2sin 2x #

# = 4 * 4sin ^ 2x * cos ^ 2 x * 2sin ^ 2x = 32sin ^ 4x * cos ^ 2 x = LHS #