Eliminate `theta`, `acottheta+bcosectheta=x^2`,`bcottheta+acosectheta=y^2`

Eliminate theta x=a sintheta , y=a costheta

Eliminate theta x=r costheta , y=r sintheta

Eliminate theta and phi sintheta +costheta =x , tantheta +cottheta=y

Eliminate theta , x=a cos^3theta , y=b sin^3theta

Eliminate theta and phi x costheta+y sintheta=a , y costheta-x sintheta=b

Eliminate theta , if tantheta+sintheta=x , tantheta-sintheta=y

Eliminate theta and phi x sintheta=a , y tantheta=b

Prove the following sec^2theta+ cosec^2theta= sec^2theta*cosec^2theta

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

If tan^2 theta=1-e^2 then prove that sec theta+tan^3 theta cosec theta=(2-e^2)^(3/2)