Question

If $3\tan \theta =4$, evaluate $(3\sin \theta +2\cos \theta )/(3\sin \theta -2\cos \theta )$.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$3\tan \theta =4$

$\tan \theta =\frac{4}{3}$

Thus, $\frac{3\sin \theta +2\cos \theta }{3\sin \theta -2\cos \theta }=\frac{3\tan \theta +2}{3\tan \theta -2}$

$=\frac{3\times 4/3+2}{3\times 4/3-2}=\frac{6}{2}=3$