Решить[latex] \sqrt{sinx} + \sqrt{cosx} =1[/latex]

[latex]\sqrt{sinx}+\sqrt{cosx}=1[/latex]   [latex]\sqrt{sinx}+\sqrt{cosx}=1\\\\ \sqrt{sinx}+\sqrt{\sqrt{1-sin^2x}}=1\\\\ \sqrt{sinx}+\sqrt[4]{1-sin^2x}=1\\\\ \sqrt{sinx}=t\\\\ t^2=sinx\\\\ \sqrt[4]{1-t^4}+t=1\\ 1-t^4=(1-t)^4\\ 2t(t-1)(t^2-t+2)=0\\ t=0\\ t=1\\ \left \{ {{sinx=0} \atop {sinx=1}} \right.\\ x=\pi*k\\ x=\frac{\pi}{2}+2\pi*k [/latex]