(D) We know that the expression $a \sin x + b \cos x$ lies in the interval $[-\sqrt{a^2 + b^2}, \sqrt{a^2 + b^2}]$.Here, $a = \sqrt{3}$ and $b = 1$.Th

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(D) We know that the expression $a \sin x + b \cos x$ lies in the interval $[-\sqrt{a^2 + b^2}, \sqrt{a^2 + b^2}]$.Here, $a = \sqrt{3}$ and $b = 1$.Thus, the maximum value of $\sqrt{3} \sin x + \cos x$ is $\sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3 + 1} = \sqrt{4} = 2$.Since the maximum value of the expression is $2$, it can never equal $4$.Therefore, the equation $\sqrt{3} \sin x + \cos x = 4$ has no solution.

Class 11 Mathematics Trigonometrical Equations Solution of trigonometrical equations

Medium

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

WBJEE 2009 All WBJEE

AP EAMCET 2001 All AP EAMCET

A
only one solution
B
two solutions
C
infinitely many solutions
D
no solution

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