Prove that following `3sintheta-sin3theta=(4sintheta)/(1+cot^2theta)`

Prove the following : (sintheta+sin3theta+sin5theta+sin7theta)/(costheta+cos3theta+cos5theta+cos7theta) = tan4theta

Prove the following (sintheta-2sin^3theta) /(2cos^3theta-costheta) =tantheta

Solve the following equation: sintheta+sin5theta=sin3theta

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

(sin3theta-cos3theta)/(sintheta+costheta)+1 =

Solve the following equation: sin3theta-sintheta=4cos^2theta-2

Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=(1-2sin^2thetacos^2theta)/(sintheta\ costheta)

Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costheta+sintheta)+(cos^(3)theta-sin^(3)theta)/(costheta-sintheta)=2

Prove the following identities: (sin^3theta+cos^3theta)/(sintheta+costheta)+sinthetacostheta=1

Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(cos^2theta)=2((1+sin^2theta)/(1-sin^2theta))