Question

решите уравнение: корень из 3 sin x + cos x=1

Answer 1

$sqrt3sinx+cosx=1 |:sqrt{(sqrt{3)^{2}+1^{2}}}=2\ frac{sqrt3}{2}sinx+frac{1}{2}cosx=frac{1}{2}\ cosfrac{pi}{6}sinx+sinfrac{pi}{6}cosx=frac{1}{2}\ sin(frac{pi}{6}+x)=frac{1}{2}\ frac{pi}{6}+x=(-1)^{k}*frac{pi}{6}+{pi}k\ 1. frac{pi}{6}+x=frac{pi}{6}+2{pi}k\ 2. frac{pi}{6}+x}={pi}-frac{pi}{6}+2{pi}n\ 1. x_1=2{pi}k\ 2. x_2=frac{2pi}{3}+2{pi}n$