Question

If $x=\sqrt{a}\sin \alpha$ and $y=\sqrt{a}\cos \alpha$, what is the value of $x^2+y^2$?

• A. $a$
• B. $\alpha$
• C. $a+\alpha$
• D. $a^2$

Answer 1

The correct option is A $a$

$x=\sqrt{a}\sin \alpha$ ; $y=\sqrt{a}\cos \alpha$
$x^2=a{\sin }^2\alpha$ ; $y^2=a{\cos }^2\alpha$
$x^2+y^2=a({\sin }^2\alpha +{\cos }^2\alpha )=a$