Q1. [1] § Introduction to Trigonometry (Chapter Header and Quote)
If $7\cos^2\theta + 3\sin^2\theta = 4$, then the value of $\theta$ is :
- A $30^\circ$
- B $45^\circ$
- C $60^\circ$
- D $90^\circ$
Previously asked in CBSE board exam
2025 30/2/1 Q1
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer
(C) 60°
$7\cos^2\theta + 3\sin^2\theta = 4 \Rightarrow 7\cos^2\theta + 3(1-\cos^2\theta) = 4 \Rightarrow 4\cos^2\theta = 1 \Rightarrow \cos\theta = \dfrac{1}{2} \Rightarrow \theta = 60°$
Explanation
Replace $\sin^2\theta$ with $1-\cos^2\theta$, simplify to get $\cos\theta = \frac{1}{2}$, which gives $\theta = 60°$. This is a standard identity-based MCQ; remember the standard angle values table from Chapter 8.
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