Question

The equation $\sqrt{3}\sin x+\cos x=4$ has

• A. Infinitely many soultions
• B. No Solutions
• C. Two solutions
• D. Only one solution

Answer 1

The correct option is B No Solutions

We know that,
$-\sqrt{a^2+b^2}\le a\cos \theta +b\sin \theta \le \sqrt{a^2+b^2}$
$\therefore -\sqrt{3+1}\le \sqrt{3}\sin x+\cos x\le \sqrt{3+1}$
$\Rightarrow -2\le \sqrt{3}\sin x+\cos x\le 2$
But, $\sqrt{3}\sin x+\cos x=4$
$\therefore$ The given equation has no solution.