Question

若f(x)=2tanx+(2sin²(x/2)-1)/(sin(x/2)cos(x/2),则f（π/12）=?

Answer 1

恒等式sin²x+cos²x=1

这个很有用,一定要记住

而sin2x=2sinxcosx

所以2(sin²x+cos²x)/sinxcosx

=4×1/(2sinxcosx)

=4/sin2x

f(x)=4/sin2x

所以f(π/12)=4/sin(2×π/12)

=4/sin(π/6)

=4/(1/2)

=8