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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
If $4\tan\theta = 3$ then $\frac{4\sin\theta-\cos\theta}{{4\sin\theta+\cos\theta}}$ is equal to :
  • A
    $\frac{3}{4}$
  • ✓
    $\frac{1}{2}$
  • C
    $\frac{1}{3}$
  • D
    $\frac{2}{3}$
✓

Answer

Correct option: B.
$\frac{1}{2}$
Given : $4\tan\theta = 3$
Dividing all terms of $\frac{4\sin\theta-\cos\theta}{{4\sin\theta+\cos\theta}}$ by $\cos\theta$
$=\frac {4\tan\theta-1}{4\tan\theta+1} = \frac{3-1}{3+1} $
$= \frac{2}{4} = \frac{1}{2}$

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