$\sin \theta +\sqrt{3}\cos \theta =6x-x^2-11,0\le \theta \le 4\pi ,x\in R$ holds for

Important Questions on Trigonometric Equations and Inequations

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 2

$\sqrt{\cos 2x}+\sqrt{1+\sin 2x}=2\sqrt{\sin x+\cos x}$, if

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 3

The solution of the system of equations ${\left|\sin x+\cos x\right|}^{{\sin }^{2}x-\frac{1}{4}}=1+\left|\sin y\right|$ and ${\cos }^{2}y=1+{\sin }^{2}y$ are

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 4

$2{\sin }^{2}x+{\sin }^{2}2x=2,-\pi <x<\pi$, then $x$ equals

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 6

If ${\left|\cos x\right|}^{{\sin }^{2}x-\frac{3}{2}\sin x+\frac{1}{2}}=1$, then possible values of $x$ are given by

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 7

The general solution of the equation $2^{\cos 2x}+1=3\cdot {\left(2\right)}^{-{\sin }^{2}x}$ is

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 8

If $4{\cos }^2\theta +\sqrt{3}=2\left(\sqrt{3}+1\right)\cos \theta$, then general value of $\theta$ is given by

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 9

The number of solutions of the equation $\sin 2x+\sin 3x+\sin 4x+\dots +\sin nx=n-1$ is

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 12 - Trigonometric Equations and Inequations>EXERCISE>Q 10

If $\sin x+\cos x=\sqrt{y+\frac{1}{y}},x\in \left(0,\pi \right)$, then