Question

Решите тригонометрическое уравнение: √3sinx+cosx=√2

Answer 1

 √3sinx+cosx=√2

√3/2sinx+1/2cosx=√2/2
sinπ/6sinx+cosπ/6cosx=√2/2
cos(x-π/6)=√2/2
 (x-π/6)=±arcos√2/2+2πn(n ∈ Z)
x=±π/4+π/6 +2πn(n ∈ Z)
x=5π/12+2πn(n ∈ Z)
и
x=-π/12+2πn(n ∈ Z)