Question

If $x=2\cos \theta -\sin \theta ;y=\cos \theta -3\sin \theta ,$ then the value of $(3x-y{)}^2+(x-2y{)}^2$ is

• A. 0
• B. 1
• C. 25
• D. 5

Answer 1

The correct option is C 25

Given,

$x=2\cos \theta -\sin \theta$

$y=\cos \theta -3\sin \theta$

$\therefore x-2y=5\sin \theta$

So, $(3x-y{)}^2+(x-2y{)}^2=25{\cos }^2\theta +25{\sin }^2\theta =25[\because {\sin }^2\theta +{\cos }^2\theta =1]$

Hence, correct option is C.