The equation 3 x + x = 4 has - Vidyadip

MCQ

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

A
Only one solution
B
Two solutions
C
Infinitely many solutions
✓
No solution

✓

Answer

Correct option: D.

No solution

d
(d) 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.

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