HOw to complete the identity of tan(theta/2)-cot(theta/2)?

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Answer 1 · 2018-03-28T20:22:12

#-2cottheta#

We know that,

#color(red)((1)tanx=sinx/cosx andcotx =cosx/sinx#

#color(red)((2)cosx=cos^2(x/2)-sin^2(x/2)#

#color(red)((3)sinx=2sin(x/2)cos(x/2)#

So,

#tan(theta/2)-cot(theta/2)=sin(theta/2)/cos(theta/2)- cos(theta/2)/sin(theta/2) ......to Apply (1)#

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

#=-(cos^2(theta/2)-sin^2(theta/2))/(2sin(theta/2)cos(theta/2))xx2#

#=-costheta/sinthetaxx2......to Apply,(2) and (3)#

#=-2cottheta#