Trigonometric Equations · Mathematics · AP EAPCET

If $\tan \left(\frac{\pi}{4}+\alpha\right)=\tan ^3\left(\frac{\pi}{4}+\beta\right)$, then $\tan (\alpha+\beta) \cot (\alpha-\beta)=$

If $0 \leq x \leq 3$ and $0 \leq y \leq 3$, then the number of solutions $(x, y)$ of the equation $\left(\sqrt{\sin ^2 x-\sin x+\frac{1}{2}}\right) 2^{\sec ^2 y}=1$ is

Statement I In the interval $[0,2 \pi]$, the number of common solutions of the equations $2 \sin ^2 \theta-\cos 2 \theta=0$ and $2 \cos ^2 \theta-3 \sin \theta=0$ is two.

Statement II The number of solutions of $2 \cos ^2 \theta-3 \sin \theta=0$ in $[0, \pi]$ is two.

The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is

$$ \tan \frac{2 \pi}{7} \cdot \tan \frac{4 \pi}{7}+\tan \frac{4 \pi}{7} \cdot \tan \frac{\pi}{7}+\tan \frac{\pi}{7} \cdot \tan \frac{2 \pi}{7}= $$

If $\sqrt{3} \cos \theta+\sin \theta>0$, then

The general solution satisfying both the equations $\sin x=-\frac{3}{5}$ and $\cos x=-\frac{4}{5}$ is

The number of solutions of the equation $\sec x \cdot \cos 5 x+1=0$ in the interval $[0,2 \pi]$ is

If $2 \sin x-\cos 2 x=1$, then $\left(3-2 \sin ^2 x\right)=$

If $x \neq(2 n+1) \frac{\pi}{4}$, then the general solutions of $\cos x+\cos 3 x=\sin x+\sin 3 x$ is

The number of solutions of $\sin 2 x+\cos 4 x=2$ in the interval $[-\pi, \pi]$ is

Number of solutions of the equation $\cos \theta+\cos 2 \theta-\sqrt{3}(\sin \theta+\sin 2 \theta)+1=0$ lying in the interval $(0,2 \pi)$ is

The number of solutions of the equation $2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta$ lying in the intervals $(-\pi, \pi)$ is

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

The general solution of

$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$

$$\text { If } \sin \theta+\operatorname{cosec} \theta=4, \text { then } \sin ^2 \theta+\operatorname{cosec}^2 \theta=$$

If $$2 \cosh 2 x+10 \sinh 2 x=5$$, then $$x=$$

If $$\sin \left(\frac{\pi}{4} \cos \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$$, then $$\theta$$ is equal to

If $$\theta \in[0,2 \pi]$$ and $$\cos 2 \theta=\cos \theta+\sin \theta$$, then the sum of all values of $$\theta$$ satisfying the equation is

The value of $$x$$ satisfying the equation $$3 \operatorname{cosec} x=4 \sin x$$ are