Question

In a $△ABC,cosA=\frac{3}{5}andcosB=\frac{5}{13}$ The value of cot C can be

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

$tanA=\frac{4}{3}andtanB=\frac{12}{5}$ Clearly tan C should be such
That tan A+tan B+tan C=tan A tan B tan C
$\therefore \frac{4}{3}+\frac{12}{5}+tanC=\frac{4}{3}.\frac{12}{5}.tanC$
Or $\frac{56}{15}+tanC=\frac{16}{5}.tanC$
$\Rightarrow tanC=\frac{56}{33}$
$\therefore cotC=\frac{33}{56}$