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

Prove that: 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)-13=0.

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)

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

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

Prove that (sintheta+cosectheta)^2+(costheta+sectheta)^2ge9 .

If sectheta=(13)/5 , show that (2sintheta-3costheta)/(4sintheta-9costheta)=3

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

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