Prove the following:`(sintheta+cosectheta)^2+(costheta+sectheta)^2=Tan^2theta+cot^2theta+7`

Prove the following identities: (sintheta+sectheta)^2+(costheta+cosectheta)^2=(1+cosecthetasectheta)^2

Prove the following: tan^2theta-sin^2theta=Sin^4thetasec^2theta

Prove the following: sqrt(2+sqrt(2+2cos4theta))=2costheta

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

Prove the following: 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4theta

Prove the following: (frac(1-cos2theta)(1+cos2theta))=tan^2theta

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

Prove that : (sin theta)/(1 - costheta) = cosec theta + cot theta

Prove the following identities: (1+cottheta-cosectheta)(1+tantheta+sectheta)=2