Multiple choice

In a $\displaystyle \Delta ABC,\tan A$ and $\displaystyle \tan B$ are the roots of the equation $\displaystyle ab\left ( x^{2}+1 \right )=c^{2}x,$ where $a,b$ and $c$ are the sides of the triangle. Then

  1. $\displaystyle \tan \left ( A-B \right )=-\frac{a^{2}+b^{2}}{2ab}$
  2. $\displaystyle \cot C=0$
  3. $\displaystyle \sin ^{2}A+\sin ^{2}B=1$

  4. none of these
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