Даю 50 баллов!! помогите пожалуйста

[latex]1)\quad tg(arcsin \frac{1}{3} )= \frac{sin(arcsin \frac{1}{3} )}{cos(arcsin \frac{1}{3} )} = \frac{ \frac{1}{3} }{\sqrt{1-sin^2(arcsin \frac{1}{3} )}} =\\\\= \frac{1}{3\cdot \sqrt{1- \frac{1}{9} }} = \frac{1}{3\frac{\sqrt{8}}{9}} =\frac{1}{\sqrt8}=\frac{1}{2\sqrt2}[/latex] [latex]2)\quad a)\; \; \; sinx=-\frac{\sqrt2}{2}\\\\x=(-1)^{n}\cdot (- \frac{\pi }{4} )+\pi n=(-1)^{n+1}\cdot \frac{\pi }{4}+\pi n ,\; n\in Z\\\\b)\; \; 3sinx=0,1\\\\sinx=\frac{1}{30}\\\\x=(-1)^{n}\cdot arcsin \frac{1}{30}+\pi n,\; n\in Z\\\\c)\; \; (1-2cosx)(sin4x+1)=0\\\\cosx=\frac{1}{2}\quad ili\quad sin4x=-1\\\\\underline {x_1=\pm \frac{\pi }{3}+2\pi n,\; n\in Z}\; \; \; \; \; ili\; \; \; \; \; 4x=-\frac{\pi }{2}+2\pi k,\; k\in Z\\\\\underline {x_2=-\frac{\pi }{8}+\frac{\pi k}{2}\; ,\; k\in Z}\\\\d)\; \; 1-2sinx\cdot cosx=0[/latex] [latex]1-sin2x=0\\\\sin2x=1\\\\2x=\frac{\pi}{2}+2\pi n,\; n\in Z\\\\x=\frac{\pi}{4}+\pi n,\; n\in Z[/latex]