Introduction to Trigonometry and Its Applications
NCERT Exemplar
CBSE
Grade 10
Question:
If $4 \tan \theta = 3$, then $\dfrac{4 \sin \theta - \cos \theta}{4 \sin \theta + \cos \theta}$ is equal to:
(a) $\dfrac{2}{3}$
(b) $\dfrac{1}{3}$
(c) $\dfrac{1}{2}$
(d) $\dfrac{3}{4}$
Step-by-Step Solution
Key Concept: Divide numerator and denominator by $\cos \theta$ to express in terms of $\tan \theta = 3/4$.
Expression $= \dfrac{4 \tan \theta - 1}{4 \tan \theta + 1}$. [0.5 Mark]
Since $4 \tan \theta = 3$: $\dfrac{3 - 1}{3 + 1} = \dfrac{2}{4} = \dfrac{1}{2}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Expressing in terms of $4 \tan \theta$: 0.5 Mark
Substituting $4 \tan \theta = 3$ to get $1/2$: 0.5 Mark
Correct Answer: $\dfrac{1}{2}$
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