If `xsin^3theta+ycos^3theta-sinthetacostheta` and `xsintheta=ycostheta,` prove that `x^2+y^2=1`

Explanation

` xsin^(3) theta + y cos^(3) theta = sin theta cos theta `
` rArr (xsin theta)sin^(2)theta + (ycos theta )cos^(2)theta = sin theta cos theta `
` rArr (xsin theta)sin^(2)theta + (xsin theta)cos^(2)theta = sin theta cos theta " " [because y cos theta = x sin theta ] `
`rArr (xsin theta ) (sin^(2) theta + cos^(2) theta ) = sin theta cos theta `
` rArr xsin theta = sin theta cos theta " " [ because sin^(2) theta + cos^(2) theta =1 ] `
` rArr x= cos theta . " "...(i) `
Now ,`xsin theta = y cos theta `
`rArr cos theta sin theta = y cos theta " "[because x= cos theta] `
` rArr y= sin theta. " "...(ii) `
On squaring (i) and (ii) and adding, we get ` x^(2) + y^(2) =1. `
Hence, ` x^(2) + y^(2) =1. `