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)

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