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#If,A+B+C=npi#
then prove that,#color(brown)(tanA+tanB+tanC=tanAtanBtanC)#

2 Answers
P dilip_k
Jan 12, 2018

#Given A+B+C=npi#

#=>A+B=npi-C#

#=>tan(A+B)=tan(npi-C)#

#=>(tanA+tanB)/(1-tanAtanB)=-tanC#

#=>(tanA+tanB)=-(1-tanAtanB)tanC#

#=>(tanA+tanB)=-tanC+tanAtanBtanC#

,#color(brown)(=>tanA+tanB+tanC=tanAtanBtanC)#

Shwetank Mauria
Jan 12, 2018

Please see below.

Explanation:

As #A+B+C=npi#

#A+B=npi-C#

and #tan(A+B)=tan(npi-C)#

or #(tanA+tanB)/(1-tanAtanB)=-tanC#

or #tanA+tanB=-tanC+tanAtanBtanC#

or #tanA+tanB+tanC=tanAtanBtanC#

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