Question

Решите систему уравнений
$left { {{sin x + frac{1}{cos y} =3} atop { frac{sin x}{cos y} = 2}} right.$

Answer 1

sinx/cosx=2
sinx=2cosy,cosy≠0⇒y≠π/2
2cosy+1/cosy=3
cosy=a
2a²-3a+1=0
D=9-8=1
a1=(3-1)/4=1/2⇒cosy=1/2⇒y=+-π/3
sinx=1⇒x=π/2