NDA 1 2025 Maths, question 45

Topic: Trigonometry

Passage · Q44 to Q45

Let $2\sin\alpha + \cos\alpha = 2$ , where $0 < \alpha < 90^{\circ}$ .

Q45

What is $2\sin 2\alpha + \cos 2\alpha$ equal to?

(a) $11/10$
(b) $11/5$ Correct answer
(c) $12/5$
(d) $13/5$

Solution.

Answer: (b) $11/5$

From $2\sin\alpha + \cos\alpha = 2$ and the acute-angle restriction, $\sin\alpha = 3/5$ and $\cos\alpha = 4/5$ .
Thus $\sin 2\alpha = 24/25$ and $\cos 2\alpha = 7/25$ .
Therefore $2\sin 2\alpha + \cos 2\alpha = 48/25 + 7/25 = 11/5$ .