Given the vector a = (cosx, SiNx) B = (cosx, - 2) C = (- 1, - 1), where x belongs to R (1), find the maximum value of FX = a * B, and find the set of X at this time (2) Find the maximum absolute value of a-c,

Given the vector a = (cosx, SiNx) B = (cosx, - 2) C = (- 1, - 1), where x belongs to R (1), find the maximum value of FX = a * B, and find the set of X at this time (2) Find the maximum absolute value of a-c,

【1】
f(x)=cos²x－2sinx=－sin²x－2sinx＋1=－(sinx＋1)²＋2
Then the maximum value of F (x) is 2, where SiNx = - 1, that is, x = 2K π - π / 2, where k ∈ Z
【2】
|If a | = 1, | C | = √ 2, and a * C = - cosx SiNx, then:
(a－c)²=|a|²－2a*c＋|c|²=3＋2(cosx＋sinx)=3＋2√2sin(x＋π/4)
Then:
The maximum value of (A-C) &# 178 is 3 + 2 √ 2 = (√ 2 + 1) &# 178;
That is, the maximum value of | a-c | is √ 2 + 1