Question
In a $$\vartriangle ABC,\tan \frac{A}{2}$$ and $$\tan \frac{B}{2}$$ satisfy $$6{x^2} - 5x + 1 = 0.$$ Then
A.
$${a^2} + {b^2} > {c^2}$$
B.
$${a^2} - {b^2} = {c^2}$$
C.
$${a^2} + {b^2} = {c^2}$$
D.
None of these
Answer :
$${a^2} + {b^2} = {c^2}$$
Solution :
$$\eqalign{
& \tan \frac{A}{2} + \tan \frac{B}{2} = \frac{5}{6},\tan \frac{A}{2} \cdot \tan \frac{B}{2} = \frac{1}{6} \cr
& \Rightarrow \,\,\tan \left( {\frac{{A + B}}{2}} \right) = 1 \cr
& \Rightarrow \,\,A + B = 2 \times \frac{\pi }{4}. \cr} $$