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

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

Prove the following 1/(cosectheta-cottheta) -1/sintheta=1/sintheta-1/(cosectheta+cottheta)

Prove that cottheta+tantheta=secthetacosectheta

Prove that (((1+cot theta +tan theta)(sintheta-costheta))/(sec^3theta -cosec^3theta)) = (sin^2theta cos^2theta)

Prove that (1+cosectheta-cottheta)/(1+cosectheta+cottheta)=(1-costheta)/(sintheta)

Prove that sintheta/(1+costheta) + (1+costheta)/sintheta = 2cosectheta

Find the value of (sintheta)/(cosectheta)+(costheta)/(sectheta)-1

Prove that sqrt((sectheta-1)/(sectheta+1))=cosectheta-cottheta

Prove the following (cosectheta-sintheta)(sectheta-costheta)=1//(tantheta+cottheta)

Prove the following (sin theta) /(1+costheta) =(1-costheta) /(sintheta)