Question

1-tan²(x/2)÷1+tan²(x/2)​

Answer 1

$= \dfrac{1-{tan}^{2} \dfrac{x}{2}}{1+{tan}^{2} \dfrac{x}{2}}$

$= {cos}^{2}2( \dfrac{x}{2})$

$= {cos}4(\dfrac{x}{2</p><p>})$

$= {cos}2x$

Identity used:

$\dfrac{1-{tan}^{2}A}{1+{tan}^{2}A} = {cos}^{2}2A$