Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $5 \cot \theta = 3$, then the value of $\dfrac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 3 \cos \theta}$ is:
(a) $\dfrac{16}{34}$
(b) $\dfrac{16}{25}$
(c) $\dfrac{9}{16}$
(d) $\dfrac{3}{5}$
Step-by-Step Solution
Key Concept: Divide numerator and denominator by $\sin \theta$: $\dfrac{5 - 3 \cot \theta}{5 + 3 \cot \theta} = \dfrac{5 - 3(3/5)}{5 + 3(3/5)} = \dfrac{5 - 9/5}{5 + 9/5} = \dfrac{16/5}{34/5} = \dfrac{16}{34} = \dfrac{8}{17}$.
$\dfrac{5 - 9/5}{5 + 9/5} = \dfrac{16/5}{34/5} = \dfrac{16}{34}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating fraction $= 16/34$: 1.0 Mark
Correct Answer: $\dfrac{16}{34}$
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