Equation √ 3 sin x + cos x = 4 has

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Trigonometrical Equations

easy

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

A

Only one solution

B

Two solutions

C

Infinitely many solutions

D

No solution

Solution

(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.

Standard 11

Mathematics

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