Prove that the equation $2\sin x=\left|x\right|+a$ has no solution for $a\in (\frac{3\sqrt{3}-\pi }{3},\infty )$.

Prove that the equations $\sin x\cdot \sin 2x\cdot \sin 3x=1$ have no solution.

prove that the equation $k\cos x-3\sin x=k+1$ has a solution for $\text{'}x\text{'}$ for $k\in (-\infty ,4]$

Prove that the equation $3(\sin x+\cos x)-2({\sin }^{3}x+{\cos }^{3}x)=8$, has no solution.

The equation $\left|\text{sin}x\right|=\text{sin}x+3\text{has in}[0,2\pi ]$

Find the principal solution of the equation $\sin x=\frac{\sqrt{3}}{2}$.

Find number of solution of the equation $2\sin x+5{\sin }^{2}x+8{\sin }^{3}x+...\infty =1$ for $x\in [0,2\pi ]$.

Find the principal solution of the equation $\sin x=\frac{\sqrt{3}}{2}$.

For $x\in (0,\pi )$ the equation $\sin x+2\sin 2x-\sin 3x=3$ has

Find the pricnipal solution of the trigonometric equation: $\sin x=\frac{\sqrt{3}}{2}$

Find the principal and general solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$