Question

решите тригонометрическое уравнение: cos(70°+x)cos(x-20°)=1/2

Answer 1

Cos(70° + x)Cos(x - 20°) = 1/2
Cos( 90°-20° + x)Cos(x - 20°) = 1/2
Sin(-20°+x)Cos(x - 20°) = 1/2
1/2Sin(-40 + 2x) = 1/2
Sin(-20° + 2x) = 1
-20° + 2x = 90°+ 360°n, n ∈Z
2x = 110° + 360°n, n ∈Z
x = 55° + 180°n, n ∈Z