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

Prove the following identities: sin^8theta-cos^8theta=(sin^2theta-cos^2theta)(1-2sin^2thetacos^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 identities: (sin^3theta+cos^3theta)/(sintheta+costheta)+sinthetacostheta=1

Prove the following trigonometric identities: (i) (1-sin^2theta)sec^2theta=1 (ii) cos^2theta(1+tan^2theta)=1

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

Prove the following identity: (2sinthetacostheta-costheta)/(1-sintheta+sin^2theta-cos^2theta)=cottheta

Prove the following trigonometric identities: cos^2theta+1/(1+cot^2theta)=1 (ii) 1/(1+sintheta)+1/(1-sintheta)=2sec^2theta

Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0 sin^6theta+cos^6theta+3sin^2thetacos^2theta=1 (sin^8theta-cos^8theta)=(sin^2theta-cos^2theta)(1-2s in^2thetacos^2theta)