Question

if x=2 sin²teta, y=2 cos²teta then find x and y​

Answer 1

x²+y²

(a sin theta+ b cos theta)² + (a cos theta+ b sin theta)²

=(a²sin²theta+b²cos²theata+ab sin theta cos theta )+(a²cos²theta+b²sin²theta-ab sin theta cos theta) using (a+b)²=a²+b²+2ab,(a-b)²=a²+b²-2ab

=a²(sin²theta+cos²theta)+b²(sin²theta + cos²theata)

=a²+b²(sin²theta+cos²theta=1)