Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

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