Question

If $x\cos \theta +y\sin \theta =2$ and $x\sin \theta -y\cos \theta =\sqrt{2}$, then $x^2+y^2=$

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is C 6

Given

$x\cos \theta +y\sin \theta =\mathrm{2.....}\left(1\right)$

$x\sin \theta -y\cos \theta =\sqrt{2}......\left(2\right)$

Squaring and adding (1) and(2)

$\Rightarrow (x\cos \theta +y\sin \theta {)}^2+(x\sin \theta -y\cos \theta {)}^2=2^2+(\sqrt{2}{)}^2$

$\Rightarrow x^2+y^2=6$