1. Tardigrade
  2. Question
  3. Mathematics
  4. In triangle A B C, if sin A cos B=(1/4) and 3 tan A= tan B, then cot 2 A is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Trigonometric Functions

Solution:

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