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

Q1. [1] § 8.4 Trigonometric Identities § 8.5 Summary
$(\cot\theta + \tan\theta)$ equals:
  1. A $\cosec\theta \cdot \sec\theta$
  2. B $\sin\theta \cdot \sec\theta$
  3. C $\cos\theta \cdot \tan\theta$
  4. D $\sin\theta \cdot \cos\theta$
Previously asked in CBSE board exam
2025 30/3/1 Q9
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer

Option A: $\cosec\theta \cdot \sec\theta$

$\cot\theta + \tan\theta = \dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta} = \dfrac{\cos^2\theta + \sin^2\theta}{\sin\theta\cos\theta} = \dfrac{1}{\sin\theta\cos\theta} = \cosec\theta \cdot \sec\theta$

Explanation

Examiners expect you to convert cot θ and tan θ into sin/cos form, add the fractions, then apply the identity sin²θ + cos²θ = 1. The result 1/(sinθ cosθ) directly equals cosec θ · sec θ. Always show the key steps even in MCQs if justification is asked.

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