Trigonometric Inequations

Solve, $\sin x>0 \& \cos x<0$, $x\in (0,2\pi )$

Solve, $\sin x+\tan x>0$, $x\in \left(0, \frac{\pi }{2}\right)$

Solve $\left|\cos x\right|\le \frac{1}{2}$

Solve ${\tan }^{3}x-{\tan }^{2}x-3\tan x+3>0$

If the equation $x^2+2x+2+e^{\alpha }-2\sin \beta =0$ has a real solution, then $(n\in Z)$:

The solution set of the inequality $\sqrt{5-2\sin x}\ge 6\sin x-1$ is $\left[2n\pi ,2n\pi +{\theta }_1\right]\cup [2n\pi +{\theta }_2,2n\pi +2\pi )(n\in Z)$ then find the value of $\frac{{\theta }_1+{\theta }_2}{\pi }$, given that ${\theta }_1$ is an acute angle and ${\theta }_2$ is an obtuse angle.

Let $\mathrm{\theta }\in [0, 2\mathrm{\pi }],$ then find the number of integral values of $\mathrm{\theta }$ satisfying $\cos \left(\mathrm{sin\theta }\right)>\sin \left(\mathrm{cos\theta }\right)$.

The set of all $x$ in $\left(0,\mathrm{\pi }\right)$ satisfying $\left|4\cos x-1\right|<\sqrt{5}$ is given by $\left(a\mathrm{\pi },\mathrm{b}\pi \right)$, then $a+b=$

If $\frac{A}{\cos \left(x+{\displaystyle \frac{2\mathrm{\pi }}{3}}\right)}=\frac{B}{\cos x}=\frac{C}{\cos \left(x-{\displaystyle \frac{2\mathrm{\pi }}{3}}\right)}$ and $\sin \theta >A+B+C$, then $\theta \in$

If ${\theta }_1,{\theta }_2,{\theta }_3\mathit{\in }[0,3\pi ]$, then the number of ordered triplets $\left({\theta }_1,{\theta }_2,{\theta }_3\right)$ which satisfy $\left(1+{cosec}^4{\theta }_1\right)\left(2+{\cot }^4{\theta }_2\right)\left(4+\sin 4{\theta }_3\right)\le 12{\sin }^2{\theta }_1$ are

The complete interval of values of $x$ in $\left(-\frac{\pi }{2}, \frac{\pi }{2}\right)$ satisfying the inequality $\cos x·\cos 2x>-\frac{1}{4}$ and $3\cos x>1,$ is

The complete interval of values of $x$ in $\left(-\frac{\pi }{2}, \frac{\pi }{2}\right)$ satisfying the equations $\cos x·\cos 2x>-\frac{1}{4}$ and $3 \cos \mathrm{x}>1,$ is

The number of integral value of $x\mathit{\in }(0, 2\pi )$ for which $\frac{|\tan x-\sin x|-|\tan x+\sin x|}{|\sin x|}\ge 2$ is (wherever defined)

Which of the following inequality is not correct?

It is given that $2\tan 2x>3\tan x \& \tan x>0$. The set of all values of $x$ satisfying both the given inequalities is $\left(m\pi ,n\pi \right)\cup \left(0,p\pi \right)$ where $m, n<0$ and $p>0$ are real numbers. Then the value of $m-n+p$ is equal to

The solution set of the system of inequations $2{\sin }^{2}x-3\sin x+1\le 0$ and $x^2+x-12\le 0$ has

The expression $\cos 3\theta +\sin 3\theta +(2\sin 2\theta -3)(\sin \theta -\cos \theta )$ is positive for all $\theta$ in

If $\sin x+\sin y\ge \cos \alpha \cos x \forall x\in R$, then $\sin y+\cos \alpha$ is equal to ________ .

The solution set of $x\in \left(-\pi ,\pi \right)$ for the inequality $\sin 2x+1\le \cos x+2\sin x$ is

The equation $\mathrm{t}\mathrm{a}{\mathrm{n}}^{4}x-2\mathrm{s}\mathrm{e}{\mathrm{c}}^{2}x+a^2=0$ will have at least one solution, if