Question

The number of solutions of $2\,\sin x + \cos\, x = 3$ is

• A. 1
• B. 2
• C. infinite
• D. No solution

Answer 1

Answer: (D)

No solution

Answer 2

Given, $2 \sin x+\cos x=3$
LHS $=2 \sin x+\cos x$
Since, $-\sqrt{5} \leq 2 \sin x+\cos x \leq \sqrt{5}$
But $\sqrt{5}<3$
Hence, no solution exist.