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Introduction of Trigonometry and its Application — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry and its Application1 Mark
MCQ
Choose the correct answer from the given four options. If $4\tan\theta=3,\text{then}\Big(\frac{4\sin\theta-\cos\theta}{4\sin\theta+\cos\theta}\Big)$ is equal to:
  • A
    $\frac{2}{3}$
  • B
    $\frac{1}{3}$
  • ✓
    $\frac{1}{2}$
  • D
    $\frac{3}{4}$
✓

Answer

Correct option: C.
$\frac{1}{2}$
$\text{Given, }4\tan\theta=3$
$\Rightarrow\tan\theta=\frac{3}{4}\ \ ...(\text{i})$
$\therefore\ \frac{4\sin\theta-\cos\theta}{4\sin\theta+\cos\theta}=\frac{4\frac{\sin\theta}{\cos\theta}-1}{4\frac{\sin\theta}{\cos\theta}+1}$
[divide by $\cos\theta$ in both numerator and denominator]
$=\frac{4\tan\theta-1}{4\tan\theta+1}$ $\bigg[\because\ \tan\theta=\frac{\sin\theta}{\cos\theta}\bigg]$
$=\frac{4\big(\frac{3}{4}\big)-1}{4\big(\frac{3}{4}\big)+1}=\frac{3-1}{3+1}=\frac{2}{4}=\frac{1}{2}$ [put the value from Eq.(i)]

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