Prove: `(1+sectheta)/(sectheta)=(sin^2theta)/(1-costheta)`

Prove the following (1 + sectheta) /(sectheta )=(sin^2theta) /(1-costheta)

Prove that: (sectheta-1)/(sectheta+1)=((sintheta)/(1+costheta))^2

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

Prove that: (i) (costheta)/(1-sintheta)=(1+sintheta)/(costheta) (ii) (1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta (iii) 1+(tan^(2)theta)/(1+sectheta)=sectheta

Prove that : (tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec theta

Prove that : (tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec theta

Prove that- (sectheta+tantheta)/(sec-tantheta)=((1+sintheta)/costheta)^2

Prove that : (sintheta)/(sectheta+tantheta-1)+(costheta)/("cosec"theta+cottheta-1)=1

Prove that : (sintheta)/(sectheta+tantheta-1)+(costheta)/("cosec"theta+cottheta-1)=1