Question

已知函数f(x)=cos²x-sin²x+2√3sinxcosx+1,若f(α)=2,且α∈[π/4

Answer 1

f(x)=cos²x-sin²x+2√3sinxcosx+1

=cos2x+√3sin2x+1

=2sin(2x+π/6)+1

f(a)=2

2sin(2x+π/6)+1=2

sin(2x+π/6)=1/2

2x+π/6=π/6+2kπ

x=kπ

2x+π/6=5π/6+2kπ

2x=2π/3+2kπ

x=π/3+kπ

∵α∈[π/4,π/2]

∴a=π/3