We know the vector M = (2sinx / 2, - root 3), n = (1-2sin & # 178; X / 4, cosx), where x belongs to R 1. If M is perpendicular to N, find the set of values of X 2. If f (x) = m * n-2t, when x belongs to [0, π], the function f (x) has two zeros, and the value range of real number T is obtained

We know the vector M = (2sinx / 2, - root 3), n = (1-2sin & # 178; X / 4, cosx), where x belongs to R 1. If M is perpendicular to N, find the set of values of X 2. If f (x) = m * n-2t, when x belongs to [0, π], the function f (x) has two zeros, and the value range of real number T is obtained

(1)
m.n=0
(2sin(x/2),-√3).( 1- 2(sin(x/4))^2,cosx) =0
2sin(x/2).[ 1- 2(sin(x/4))^2] -√3cosx =0
2sin(x/2) cos(x/2)-√3cosx =0
sinx-√3cosx =0
tanx = √3
x = kπ+ π/3 k=0,1,2,.
(2)
f(x)=0
m.n -2t =0
sinx-√3cosx - 2t =0
2sin(x-π/3) -2t =0
t = sin(x-π/3)
0