Question

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

• A. True
• B. False

Answer 1

The correct option is A True

Given, $x=a\cos \theta +b\sin \theta$......(1) and $y=a\sin \theta -b\cos \theta$......(2).

Now squaring (1) and (2) and then adding we get,

$x^2+y^2=a^2({\cos }^2\theta +{\sin }^2\theta )+2ab\sin \theta .\cos \theta -2ab\sin \theta .\cos \theta +b^2({\sin }^2\theta +{\cos }^2\theta )$

or, $x^2+y^2=a^2+b^2$.