Question

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

Answer 1

$\tan A=1$

$\Rightarrow A={45}^o$

$\Rightarrow \sin A=\frac{1}{\sqrt{2}}$, $\cos A=\frac{1}{\sqrt{2}}$

$\Rightarrow 2\sin A\cos A=2\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)=1$.