化简(1+cos2x)/{cot(x/2)-tan(x/2)}

问题描述:

化简(1+cos2x)/{cot(x/2)-tan(x/2)}

1+cos2x=2cosx^2
cotx/2-tanx/2
=(cosx/2^2-sinx/2^2)/(sinx/2*cosx/2)
=cosx/(0.5sinx)
所以
原式=2cosx^2/[cosx/(0.5sinx)]
=cosxsinx
=0.5sin2x