Question

If $x=\sqrt{a}\sin \alpha$ and $y=\sqrt{a}\cos \alpha$. The value of $y^2+x^2$ is

• A. a
• B. $\sqrt{a}$
• C. $a^2$
• D. $\frac{a}{2}$

Answer 1

The correct option is A

a

Given, $x=\sqrt{a}\sin \alpha$ and $y=\sqrt{a}\cos \alpha$

$\Rightarrow x^2=a{\sin }^2\alpha$ and $y^2=a{\cos }^2\alpha$

$\Rightarrow y^2+x^2=a({\cos }^2\alpha +{\sin }^2\alpha )=a$ [$\because {\sin }^2\alpha +{\cos }^2\alpha =1$]