MCQ
If $5 \tan\alpha = 4,$ then the value of. $\frac{5\sin\alpha-3\cos\alpha}{5\sin\alpha+2\cos\alpha}$ is :
- A$\frac{1}{4}$
- ✓$\frac{1}{6}$
- C$\frac{1}{5}$
- D$\frac{4}{5}$
✓
Answer
Correct option: B.
$\frac{1}{6}$
Given : $5 \tan\alpha = 4,$
Dividing all terms of $\frac{5\sin\alpha-3\cos\alpha}{5\sin\alpha+2\cos\alpha}$ by $\cos\alpha$
$=\frac {5\tan\alpha-3}{5\tan\alpha+2} = \frac{4-3}{4+2} = \frac{1}{6}$
Dividing all terms of $\frac{5\sin\alpha-3\cos\alpha}{5\sin\alpha+2\cos\alpha}$ by $\cos\alpha$
$=\frac {5\tan\alpha-3}{5\tan\alpha+2} = \frac{4-3}{4+2} = \frac{1}{6}$
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