题目

f(x)=2cos²x/2+√3(sinx)
若a为第二象限角,且f(a-π/3)=1/3,求cos2a/1-tana的值

提问时间：2021-01-11

答案

f(x)=2cos²x/2-√3sinx
=1+cosx-√3sinx
=1+2(1/2cosx-√3/2sinx)
=1+2sin(x+5π/6)
f(a-π/3)=1+2sin(a-π/3+5π/6)
=1+2*sin(a+π/2)
=1+2cosa
=1/3
cosa=-1/3
sina=2√2/3
tana=-2√2
cos2a/1-tana=(1-2√2)/9