A) infinitely many solutions
B) no solution
C) two solutions
D) only one solution
Correct Answer: B
Solution :
We know that, \[-\sqrt{{{a}^{2}}+{{b}^{2}}}\le a\cos \theta +b\sin \theta \le \sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\therefore \]\[-\sqrt{3+1}\le \sqrt{3}\sin x+\cos x\le \sqrt{3+1}\] \[\Rightarrow \]\[-2\le \sqrt{3}\sin x+\cos x\le \sqrt{2}\] But \[\sqrt{3}\sin x+\cos x=4.\] Hence, given equation has no solution.
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