1)√2sinx-1=0

[tex]sinx=\frac{1}{\sqrt{2} } ,[/tex]  [tex]sinx=\frac{\sqrt{2} }{2}[/tex]

[tex]x_1=\frac{\pi }{4} +2\pi n,[/tex] n∈Z

[tex]x_2=\frac{3\pi }{4} +2\pi m,[/tex] m∈Z

2)  [tex]tg\frac{x}{2} -\sqrt{3} =0[/tex]  , [tex]tg\frac{x}{2} =\sqrt{3}[/tex]   , [tex]\frac{x}{2} =\frac{\pi }{3} +\pi n[/tex]  |*2,

[tex]x =\frac{2\pi }{3} +2\pi n[/tex] ,n∈Z

Verified answer

[tex]\displaystyle\bf\\1)\\\\\sqrt{2} Sinx-1=0\\\\\sqrt{2} Sinx=1\\\\Sinx=\frac{1}{\sqrt{2} } \\\\x=(-1)^{n} arcSin\frac{1}{\sqrt{2} } +\pi n,n\in Z\\\\\boxed{x=(-1)^{n} \frac{\pi }{4} +\pi n,n\in Z}\\\\\\2)\\\\tg\frac{x}{2} -\sqrt{3} =0\\\\tg\frac{x}{2} =\sqrt{3} \\\\\frac{x}{2} =arctg\sqrt{3} +\pi n,n\in Z\\\\\frac{x}{2} =\frac{\pi }{3} +\pi n,n\in Z\\\\\boxed{x=\frac{2\pi }{3} +2\pi n,n\in Z}[/tex]