已知(1-cosα sinα)/(1 cosα sinα)=-2,那麽tanα的值是多少? 網友廻答:
- (1-cosα sinα)/(1 cosα sinα)
=[1-(1-2sin^2(a/2)) sina]/[1 2cos^2(a/2)-1 sina]
=[2sin^2(a/2) 2sin(a/2)cos(a/2)]/[2cos^2(a/2) 2sin(a/2)cos(a/2)]
=sin(a/2)/cos(a/2)
=tana/2
tana/2=-2
tana=tan(a/2 a/2)=(2tana/2)/(1-tana/2平方)
代入解之得tanα=4/3
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