高中数学题,第7题,解析

2025-05-16 17:29:38
推荐回答(1个)
回答(1):

f(x)=2*2tan(x/2)/[1-tan²(x/2)]+2*[1-2sin²(x/2)]/[2sin(x/2)cos(x/2)]
=2tanx+2cosx/sinx
=2(sinx/cosx+cosx/sinx)
=2(sin²x+cos²x)/sinxcosx
=4*1/(2sinxcosx)
=4/sin2x
所以f(π/12)=4/sin(π/6)=8