Prove that `(sintheta-costheta+1)/(sintheta+costheta-1)=(1+sintheta)/costheta`

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

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

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

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

Prove that (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tantheta) , using the identity sec^2theta=1+tan^2theta

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

Prove that (costheta-sintheta+1)/(costheta+sintheta-1)=c o s e ctheta+cottheta

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

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

i) Prove that: (cot^(2)A)/(1-"cosec"A)^(2)=(1+sinA)/(1-sinA) ii) Prove that: (costheta)/(1-tantheta)+(sintheta)/(1-cottheta)=sintheta+costheta