Prove the following:`cot4x(sin5x+sin3x)=cotx(sin5x-sin3x)`

Prove the following: (frac(sinx-sin3x+sin5x-sin7x)(cosx-cos3x-cos5x+cos7x))=cot2x

Prove the following: (frac(sin5x-2sin3x+sinx)(cos5x-cosx))=tanx

Prove the following: sin6x+sin4x-sin2x=4cosxsin2xcos3x

Prove the following: (frac(sin2x+sin2y)(sin2x-sin2y))=(frac(tan(x+y))(tan(x-y)))

Prove the following: (frac(cos9x-cos5x)(sin17x-sin3x))=(frac(-sin2x)(cos10x))

Select and write the correct answer from the given alternatives in each of the following: (frac(sin5x+sin3x)(cos5x+cos3x)) =

Prove the following : sin^2 6x-sin^2 4x=sin2xsin10x

Prove the following: (frac(sin3x)(cosx))+(frac(cos3x)(sinx))=2cot2x

Prove the following: (sin3x+sinx)sinx+(cos3x-cosx)cosx=0