Question

If 3 tan theta =4, then evaluate : 3sin theta + 2cos theta / 3sin theta - 2cos theta​

Answer 1

Answer:

3sin theta + 2cos theta / 3sin theta - 2cos theta = 3

Step-by-step explanation:

$\frac{3 \sinθ + 2 \cosθ}{3 \sinθ - 2 \cosθ} \\ = \frac{(3 \times \frac{4}{5}) + (2 \times \frac{3}{5})}{(3 \times \frac{4}{5}) - (2 \times \frac{3}{5})}$

$= \frac{ \frac{12}{5} + \frac{6}{5}}{ \frac{12}{5} - \frac{6}{5}} \\ = \frac{ \frac{18}{5}}{ \frac{6}{5}} \\ = \frac{18}{6} \\ = 3$