Prove that `(1+sintheta+costheta)^2=2(1+sintheta)(1+costheta)`

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

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

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

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

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

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

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