Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minPYQ_2021

MathematicsMediuminteger

If $\sqrt{3} (\cos^{2} x) = (\sqrt{3} - 1) \cos x + 1$ , then number of solutions of the given equation when $x \in [0, \frac{π}{2}]$ is ________.

Answer:

Solution:

$\sqrt{3} {(\cos x)}^{2} - \sqrt{3} \cos x + \cos x - 1 = 0$

$\Rightarrow (\sqrt{3} \cos x + 1) (\cos x - 1) = 0$

$\Rightarrow \cos x = 1$ or $\cos x = - \frac{1}{\sqrt{3}}$ (reject)

$\Rightarrow x = 0$ only

Hence, only one solution.

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2021

Loading discussions...