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If median CD of ∆ABC is perpendicular on AC then show that 2 tan A +tanC =0

If median CD of ∆ABC is perpendicular on AC then show that 2 tan A +tanC =0

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Grade:11

1 Answers

Arun
25757 Points
5 years ago
Dear Anjali
When we draw the median CD then, you will see that-
 
In Triangle BCD 
 
 use sine rule
 
c/2 sinA /sin(180-C-A)   = c/2 /sin(C-90)
 
sinA/sin(A+C)  = -1/cosC
 
 sinA cosC = -sin(A+ C)
 
 sinAcosC  =-[sinAcosC + cosA sinC]
 
 2tanA +tanC =0
 
Regards
Arun (askIITians forum expert)

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