Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minPYQ_2022

MathematicsMediumnumerical

The number of solutions of the equation $\sin x = \cos^{2} x$ in the interval $(0, 10)$ is ______.

Answer:

4.00

Solution:

Given, $\sin x = \cos^{2} x$

$\Rightarrow \sin x = 1 - \sin^{2} x$

$\Rightarrow \sin^{2} x + \sin x - 1 = 0$

$\Rightarrow \sin x = \frac{(- 1 \pm \sqrt{5})}{2}$

$\Rightarrow \sin x = \frac{(\sqrt{5} - 1)}{2}$

Now plotting the graph we get,

$\Rightarrow$ Now by graph number of solutions in $(0, 10) = 4$

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2022

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