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

Explanation

(i) `sin^(2)theta+ cos^(2)theta = x^(2)/4 + y^(2)/9=1`
(ii) `sec^(2)theta-tan^(2)theta=(x/2)^(2//3)-(y/3)^(2//3)=1`
(iii) `x^(2)+y^(2)=2`.
(iv) `2sec theta=x+1/x`
`2tan theta=x-1/x`
`tan theta=(x-1/x)/(2), sec theta=(x+1/x)/(2)`
`sec theta. tan theta=y`
`((x^(2)-1)/(2x)). ((x^(2)+1)/(2x))=y`
`x^(4)-1=4x^(2)y`