求证:(1+sinA-cosA)⼀(1+sinA+cosA)=tan(A⼀2)

2024-12-29 06:24:21
推荐回答(1个)
回答1:

证明:
(1+sina-cosa)/(1+sina+cosa)
=( 1+2sina/2cosa/2cos2a+sin2a/2)/(1+2sina/2cosa/2+cos2a/2-sin2a/2)
=(2sin2a/2+2sina/2cosa/2)/(2cos2a/2+2sina/2cosa/2) =[2sina/2(sina/2+cosa/2)]/[2cosa/2(cosa/2+sina/2)]
=(sina/2)/(cosa/2)
=tana/2