Question

If $x=a\sin \theta +b\cos \theta$ and $y=a\cos \theta -b\sin \theta$, then prove that $x^2+y^2=a^2+b^2$

Answer 1

$\begin{array}{c}x=a\sin \theta +b\cos \theta \\ y=a\cos \theta -b\sin \theta \\ Now,\\ x^2+y^2=a^2+b^2+2ab\sin \theta \cos \theta -2ab\sin \theta \cos \theta \\ x^2+y^2=a^2+b^2\\ hence,proved.\end{array}$