Show that : `(frac(sinA+sin5A+sin9A)(cosA+cos5A+cos9A))=tan5A`

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

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

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

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

(sin3A-cos(pi/2-A))/(cosA+cos(pi+3A))=

(cos7A+cos5A)/(sin7A-sin5A)=

Show that: (frac(sin3theta+2sin5theta+sin7theta)(sintheta+2sin3theta+sin5theta))=cos2theta+sin2thetacot3theta

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

Prove that (cos 9^(@)+ sin 9^(@))/(cos 9^(@) -sin 9^(@)) = tan 54^(@)