Question

If $3\sin \theta +5\cos \theta =5$, then find the value of $5\sin \theta -3\cos \theta$.

Answer 1

Answer: 3.00

$9{\sin }^2\theta +25{\cos }^2\theta +30\sin \theta \cos \theta =25$ ...(i)
$25{\sin }^2\theta +9{\cos }^2\theta -30\sin \theta \cos \theta =x^2$ ...(ii)
$\Rightarrow 9+25=x^2+25$
$\Rightarrow x=3$