Question

In triangle $ABC$, If $\sin A \cos A =\frac{1}{4}$ and $3 \tan A=\tan B$, then $\cot ^{2} A$ is equal to :

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (B), (C)

$ 3 \sin A \cos B =\sin B \cos A $
$ \Rightarrow \cos A \cos B =\frac{3}{4} $
$\Rightarrow \sin ( A + B )=1 $
$ \Rightarrow C =\frac{\pi}{2}, B =\frac{\pi}{2}- A$
$\Rightarrow 3 \tan A =\tan A \left(\frac{\pi}{2}- A \right)$
$ \Rightarrow 3=\cot ^{2} A$