Question

Evaluate:
$\frac{2\tan {45}^{\circ }}{1+{\tan }^2{45}^{\circ }}=$

Answer 1

$\begin{array}{c}\frac{2\tan {45}^{\circ }}{1+{\tan }^2{45}^{\circ }}\\ \left\{\begin{array}{c}\because \frac{2\tan {45}^{\circ }}{1+{\tan }^2{45}^{\circ }}=\sin 2\theta \\ here,\theta ={45}^{\circ }\end{array}\right\}\\ =\sin (2\times {45}^{\circ })=\sin {90}^{\circ }\\ =1\end{array}$