The equation $4{\sin }^{2}x-2\left(\sqrt{3}+1\right)\sin x+\sqrt{3}=0$ has

Important Questions on Trigonometric Equations and Inequalities

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-2>Q 15

If ${\cos }^{2}2x+2{\cos }^{2}x=1, x\in \left(-\pi ,\pi \right)$, then $x$ can take the values

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-2>Q 16

$\frac{{\sin }^3\theta -{\cos }^3\theta }{\sin \theta -\cos \theta }-\frac{\cos \theta }{\sqrt{1+{\cot }^2\theta }}-2\tan \theta \cot \theta =-1$ if

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-2>Q 17

The maximum value of ${\log }_{20}(3\sin x-4\cos x+15)$ -

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-3>Q 10

Find number of values of $x$ in the interval $\left[0, 5\pi \right]$ satisfying the equation $\frac{\sqrt{3}}{2}\sin x-\cos x={\cos }^{2}x$.

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-3>Q 11

Find number of values of $x$ in the interval $\left[0,2\pi \right]$ satisfying the equation $\cot x-2\sin 2x=1$.

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-3>Q 12

Find number of values of $x$ in the interval $\left(-2\pi ,2\pi \right)$ satisfying the equation $\sqrt{13-18 \tan x}=6\tan x-3$.

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-3>Q 13

Find number of values of $\theta$ in the interval $\left[0,\pi \right]$ satisfying the equation $\sin \theta +\sin 5\theta =\sin 3\theta$.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 13 - Trigonometric Equations and Inequalities>EXERCISE-3>Q 14

Find number of values of $\theta$ in the interval $\left[0,2\pi \right]$ satisfying the equation $\cot \theta +\mathrm{cosec}\theta =\sqrt{3}$.