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

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

Prove that ((1+sintheta)^2+(1-sintheta)^2)/(2cos^2theta)=(1+sin^2theta)/(1-sin^2theta) .

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

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Prove that-: cos^4theta/(1-sin^4theta)=(1-sin^2theta)/(1+sin^2theta)

Prove the following identities: (cos^2theta)/(1-tantheta)+(sin^3theta)/(sintheta-costheta)=1+sinthetacostheta

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

Prove the following identities: (i) costhetasin(90^o-theta)+sinthetacos(90^o-theta)=1 (ii) (sin(90^o-theta))sintheta/(tantheta)-1=-sin^2theta (iii) (sin(90^o-theta)cos(90^o-theta))/(tantheta)=1-sin^2theta

Prove the following identity : (cot^2 theta)/((1- cosec theta)^2)= (1+sin theta)/(1-sin theta) .

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