Eliminate `theta` between the equations:
`a cosec theta + bcot theta= x^2, a cot theta + b cosec theta = y^2`

Eliminate theta between the equation : x =a sec theta, y= b tan theta .

Eliminate theta between the equation : x =a sec^3 theta, y = b tan^3 theta .

Eliminate theta between the equation : x= h+a cos theta, y=k+ b sin theta .

Eliminate theta between the equation : x =a cos theta + b sin theta, y =a sin theta- b cos theta .

Eliminate theta between the equation : x = sin theta + cos theta, y = sin theta-cos theta .

Eliminate A between the equation : a cosec A +b cot A= x^2, b cosec A+ a cot A= y^2 .

Solve : sec theta-cosec theta =4/3 .

Solve the following trigonometric equation : cosec^2 theta= 2 cot theta .

If p and q are respectively the perpendiculars from the origin upon the striaght lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = a cos 2 theta , then 4p^(2) + q^(2) is equal to

Prove the following identity : cosec^6 theta- cot^6 theta =3 cot^2 theta cosec^2 theta+1 .