Question

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

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (B)

$3$

${(3\sin \theta +5\cos \theta )}^2+{(5\sin \theta +3\cos \theta )}^2$
$=9({\sin }^2\theta +{\cos }^2\theta )+25({\sin }^2\theta +{\cos }^2\theta )$
$=34$
$\therefore {(5\sin \theta -3\cos \theta )}^2=34-25=9$
$\Rightarrow (5\sin \theta -3\cos \theta )=3$