Question

Решить$sqrt{sinx} + sqrt{cosx} =1$

Answer 1

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