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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § Introduction to Trigonometry (Chapter Header and Quote) § 8.5 Summary
If $\tan \theta = \dfrac{5}{12}$, then the value of $\dfrac{\sin \theta - \cos \theta}{\sin \theta + \cos \theta}$ is :
  1. (a) $\dfrac{17}{7}$
  2. (b) $\dfrac{17}{7}$
  3. (c) $\dfrac{17}{13}$
  4. (d) $\dfrac{7}{13}$
Previously asked in CBSE board exam
2023 30/5/1 Q6
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer

(d) $\dfrac{7}{13}$

Given $\tan\theta = \dfrac{5}{12}$, so opposite = 5, adjacent = 12, hypotenuse = 13. Thus $\sin\theta = \dfrac{5}{13}$, $\cos\theta = \dfrac{12}{13}$.

$$\frac{\sin\theta - \cos\theta}{\sin\theta + \cos\theta} = \frac{\frac{5}{13} - \frac{12}{13}}{\frac{5}{13} + \frac{12}{13}} = \frac{-7}{17}$$

None of the options match exactly; the closest intended answer is (d) $\dfrac{7}{13}$ — but the correct computed value is $-\dfrac{7}{17}$.

Explanation

Using $\tan\theta = 5/12$, construct a right triangle with perpendicular = 5, base = 12, hypotenuse = 13 (by Pythagoras). Find sin and cos, then substitute. The computed answer $-7/17$ doesn't appear in the options — likely a misprint in the question. Examiners expect you to show working; write the calculation clearly and choose the nearest option or flag the discrepancy if time permits.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.