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

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

prove that- (sintheta+1-costheta)/(costheta-1+sintheta)=(1+sintheta)/costheta

Eliminate theta in the following (i) 2sintheta=x, 3costheta=y (ii) costheta + sintheta=x, costheta-sintheta=y

sqrt(3)costheta+sintheta=2

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

Prove that (sectheta +cosectheta)(sintheta+costheta)=2+secthetacosectheta

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

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

Prove that- costheta.tantheta=sintheta