Proving a trigonometric identity

Trigonometric identities

Prove the trigonometric identities: (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2

Prove the trigonometric identities: (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+tantheta+cottheta

Prove the trigonometric identities: sqrt((1-costheta)/(1+costheta))=cos e ctheta-cottheta

Prove the trigonometric identities: 1/(secA+tanA)-1/(cosA)=1/(cosA)-1/(secA-tanA)

Prove the trigonometric identities: If T_n=sin^ntheta+cos^ntheta, prove that (T_3-T_5)/(T_1)=(T_5-T_7)/(T_3)

Prove the following trigonometric identities: (sintheta)/(1-costheta)=cos e ctheta+cottheta

Prove the following trigonometric identities: (tantheta+sintheta)/(tantheta-sintheta)=(sectheta+1)/(sectheta-1)

Prove the following trigonometric identities: cottheta-tantheta=(2cos^2theta-1)/(sinthetacostheta)

Prove the following trigonometric identities: cottheta-tantheta=(2cos^2theta-1)/(sinthetacostheta)