Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

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