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

WBJEEWBJEE 2011Trigonometric Functions

Solution:

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.