Question

In a right triangle $ABC$, right angled at $B$. If $\tan A=1$ then verify that $2\sin A.\cos A=1$

Answer 1

Given in a right triangle $ABC$, right angled at $B$.

Also given $\tan A=1$.

Now,

$2\sin A.\cos A$

$=\sin 2A$

$=\frac{2\tan A}{1+{\tan }^{2}A}$

$=\frac{2\times 1}{2}$[ Using value of $\tan A$]

$=1$.