Question

Sin2x/1+cos2x=tanx How do I prove this with the double angle law

Answer 1

$sin(2x) = 2 sin x cos x \\ \\ cos(2x) = cos^2 x - sin^2 x$
After Substituting:
$\frac{2 sin x cos x}{1+cos^2 x - sin^2 x}$
Use pythagorean thm:
$1 - sin^2 x = cos^2 x$
......................
$\frac{2 sin x cos x}{2cos^2 x} \\ \\ = \frac{sinx }{cos x} \\ \\ = tan x$