$x = a Cos heta + b Sin heta$ $y = a Sin heta - b Cos heta$ $x^2 + y^2$ is equal to-

Question

$x = a Cos	heta + b Sin	heta$ $y = a Sin	heta - b Cos	heta$ $x^2 + y^2$ is equal to-

CIVILSHUB IAS · Accepted Answer

$a^2 + b^2$. $x = a Cos	heta + b Sin	heta$ $x^2 = (a Cos	heta + b Sin	heta)^2$ $y = (a Sin	heta - b Cos	heta)$ $y^2 = (a Sin	heta - b Cos	heta)^2$ $x^2 + y^2 = (a Cos	heta + b Sin	heta)^2 + (a Sin	heta - b Cos	heta)^2$ $= a^2 (Sin^2	heta + Cos^2	heta) + b^2 (sin^2	heta + Cos^2	heta)$ $+ 2ab Cos	hetaSin	heta - 2ab Sin	heta.Cos	heta$ $x^2 + y^2 = a^2 + b^2$

$x = a Cos\theta + b Sin\theta$ $y = a Sin\theta - b Cos\theta$ $x^2 + y^2$ is equal to-

Explanation