Trigonometry

In a triangle ABC, tanA + tanB + tanC = k, then for what values of k :-

a) there exists exactly one isosceles triangle ABC.
b) there exists exatly two non-similar isosceles triangle ABC.

please solve the answer..

2 Answers

Hint:

tan C = tan (Pi- A -B)

= - tan (A+B)

=-(tanA+tanB)/(1+tanAtanB)

now we need to substitute that back in the main equation..

we want an isoceles triangle..

so tan A = tan B

so we substitute that we get a quadratic..

for one isoceles triangel there has to be one real root hence D=0

for 2 ... we will have D>0

if you dont get the method or cant solve it.. do tell me i will try to do it for u :)

sir k in terms of what

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