Question

设f(x)=6cos^2x-根3sin2x

Answer 1

f(x)=6cos^2x-√3sin2x

=3(1+cos2x)-√3sin2x

=3+2√3(cosπ/6cos2x-sinπ/6sin2x)

=3+2√3cos(2x+π/6)

fmax(x)=3+2√3,

T=2π/2=π

f(a)=fmin(x),

2a+π/6=π,

a=π/2-π/12=5π/12,

4a/5=π/3,

tan4/5a=tanπ/3=√3 .