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plz help me to solve this In triangle ABC, prove the following sinA+sin(B-C)=2sinBcosC tanA+tanB+tanC=tanAtanBtanC

plz help me to solve this
 In triangle ABC, prove the following
  1. sinA+sin(B-C)=2sinBcosC
  2. tanA+tanB+tanC=tanAtanBtanC

Grade:10

1 Answers

Ajay
209 Points
4 years ago
A+B+C = 180
For  the first part put Sin A = SIn(180-(B+C) = sin(B+C)
Now SinA + Sin(B-C) = sin(B+C)+sin(B-C) = 2SinBsinC
 
for second part consider  A = 180-(B+C)
TanA=Tan(180-(B+C)=-Tan(B+C)\\ TanA\quad =\quad \frac { -TanB-Tanc }{ 1+TanC.TanB } \\ On\quad rearranging\\ TanA+TanB+TanC=\quad TanA.TanB.TanC
 

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