Question

How do you prove `tan(x) = sin(2x)/[1+cos(2x)]`?

Answer 1

Use the trig identities:
`sin 2x = 2sin x.cos x`
`(1 + cos 2x) = 2cos^2 x`
Right side:
`(sin 2x)/(1 + cos 2x) = (2sin x.cos x)/(2cos^2 x) = sin x/(cos x) = tan x.`