Trigonometric Equations

The minimum value of the expression $\sin \alpha+\sin \beta+\sin \gamma$, where $\alpha, \beta, \gamma$ are real numbers satisfying $\alpha+\beta+\gamma=\pi$ is

If $n \in N$, then $|\sin n x|$

The number of solutions of the equation $1+\sin x \cdot \sin ^2 \frac{x}{9}=0$ in $[-\pi, \pi]$ is

If $a \cos ^3 \alpha+3 a \cos \alpha \sin ^2 \alpha=m$ and $a \sin ^3 \alpha+3 a \cos ^2 \alpha \sin \alpha=n$, then $(m+n)^{2 / 3}+(m-n)^{2 / 3}$ is equal to

If $\sec A-\tan A+a=0, \sin A$ is equal to

The equation $3 \cos x+4 \sin x=6$ has ..... solution?

If $x, y \in[0,2 \pi]$ then the total number of ordered pairs $(x, y)$ satisfying $\sin x \cdot \cos y=1$ is equal to

The value of $\sum_{p=1}^6 2\left(\sin \frac{2 p \pi}{7}-i \cos \frac{2 p \pi}{7}\right)$ is

The number of values of the triplet $(a, b, c)$ for which $a \cos 2 x+b \sin ^2 x+c=0$ is satisfied by all real $x$, is

The maximum value of $\left(\cos \alpha_1\right) \cdot\left(\cos \alpha_2\right) \ldots\left(\cos \alpha_n\right) . \quad$ Under the restrictions $0 \leq \alpha_1, \alpha_2, \ldots \alpha_n \leq \frac{\pi}{2} \quad$ and…

The sum of all the solutions of the equation $\cos x \cdot \cos \left(\frac{\pi}{3}+x\right) \cdot \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4}$, $x \in[0,6 \pi]$ is

The number of values of $x$ in the interval $[0,5 \pi]$ satisfying the equation $3 \sin ^2 x-7 \sin x+2=0$ is