Question

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

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

Answer 1

Answer: (D)

No solution

Answer 2

Given equation is $\sqrt{3}\sin x + \cos x = 4$ which is of the form $a\sin x + b\cos x = c$ with $a = \sqrt{3},b = 1,c = 4$

Here $a^{2} + b^{2} = 3 + 1 = 4 < c^{2},$ Therefore the given equation has no solution.