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In \Delta ABC  if \tan \:\frac{C}{2} (a \tan A+b\tan B)=a+b   , then the triangle is 

Option: 1

Right angled 


Option: 2

Isosceles


Option: 3

Equilateral


Option: 4

Obtuse angled 


Answers (1)

best_answer

 

Transformation Formulae -

- wherein

These formula are also called A-B formulae.

 

 

\tan\frac{C}{2}(a \tan A+b \tan B)=a+b

\Rightarrow a \cos B \cos\left ( A+\frac{C}{2} \right )+b \cos A \cos \left ( B+\frac{C}{2} \right )=0

 

\Rightarrow (a \cos B- b \cos A)\cos \left ( A+\frac{C}{2} \right )=0 ,

as  \cos \left ( B+\frac{C}{2} \right )=\cos \left ( \pi-A-\frac{C}{2} \right )

\Rightarrow A=B  , in either case

 

Posted by

SANGALDEEP SINGH

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