Question

If $\sin A=\frac{3}{5}$and $0°<A<90°$, then the value of $\tan 2A$ is

• A.
  $\frac{20}{7}$
• B.
  $\frac{22}{7}$
• C.
  $\frac{24}{7}$
• D.
  $\frac{26}{7}$

Answer 1

The correct option is C

$\frac{24}{7}$
Given $\mathrm{sinA}=\frac{3}{5}$ and $A$ is the acute angle. Therefore,
$\cos A=\frac{4}{5}$
Then, $\tan A=\frac{\sin A}{\cos A}=\frac{3}{4}$.
Now, we know the identity $\tan 2A=\frac{2\tan A}{1-{\tan }^{2}A}$
Now, substituting the value of $\tan A$ in the above identity we get,
$\tan 2A=\frac{2\times 3/4}{1-9/16}=\frac{6/4}{7/16}=\frac{24}{7}$.
Thus, Option c. is correct.