Question

If $3sin\theta +4cos\theta =5,then4sin\theta -3cos\theta$ is equal to

• A. $0$
• B. $5$
• C. $1$
• D. None of these

Answer 1

The correct option is A $0$

$3\sin \theta +4\cos \theta =5$

$\frac{3}{5}\sin \theta +\frac{4}{5}\cos \theta =1$

Lets $\sin \varphi =\frac{4}{5}$

$\sin (\theta +\varphi )=1$

$\theta +\varphi =2n\pi +\frac{\pi }{2}$

Now $4\sin \theta -3\cos \theta =5\times \frac{4\sin \theta -3\cos \theta }{5}$

$=5\times \cos (\theta +\varphi )=5\times \cos (2n\pi +\frac{\pi }{2})=0$