How do you prove that # tan(x/2)-cot(x/2) = -2cotx #?

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Answer 1 · 2016-02-23T09:59:58

#tan(x/2)−cot(x/2)=-2cotx# For proof see below.

#tan(x/2)−cot(x/2)#

= #sin(x/2)/cos(x/2)-cos(x/2)/sin(x/2)#

=#(sin^2(x/2)-cos^2(x/2))/(sin(x/2)cos(x/2))#

As #cosx=cos^2(x/2)-sin^2(x/2)# and #sinx=2sin(x/2)cos(x/2)#

Above can be written as #-cosx/(sinx/2)# or

#-2cotx#