Question

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

• A. $\pm 3$
• B. $\pm 4$
• C. $\pm 5$
• D. $\pm 6$

Answer 1

Answer: (A)

$\pm 3$

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

Let $5\sin \theta -3\cos \theta =x$

Square and add both equations ;

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

$\Rightarrow 9+25=25+x^2$

$\Rightarrow x^2=9$

$\Rightarrow x=\pm 3$

$\Rightarrow 5\sin \theta -3\cos \theta =\pm 3$