Mathematical problems of triangle vector In the triangle ABC, the opposite sides of the angle ABC are ABC, vector M = (B + C, a), n = (a - √ 3C, B-C), if vector M / / N, 1. Find the size of angle B 2. The value of COS (B + 10 °) × [1 + √ 3tan (b-20 °)]

Mathematical problems of triangle vector In the triangle ABC, the opposite sides of the angle ABC are ABC, vector M = (B + C, a), n = (a - √ 3C, B-C), if vector M / / N, 1. Find the size of angle B 2. The value of COS (B + 10 °) × [1 + √ 3tan (b-20 °)]

1) M / / N, with non-zero λ∈ R, such that: M = λ n - >
b + c = λ(a-√3c)
a = λ(b - c)
-> a² - √3ca + (c² - b²) = 0
-> a² + c² - b² = √3ac
cos B=(a²+c²-b²)/(2ac) = √3ac/(2ac) = √3/2
B = π/6
2) What is the value of COS (B + 10 °) × [1 + √ 3tan (b-20 °)]?
=cos 40°×(1+√3 tan 10°)=1