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

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

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

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

(sin5x+sin3x)/(cos5x+cos3x)=

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

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

Prove the following: (frac(cosx+sinx)(cosx-sinx))-(frac(cosx-sinx)(cosx+sinx))=2tan2x

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

(sin3x-sinx)/(cos2x) =

(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x