Question

Prove? sin2x=2tanx/1+tan^2x

Answer 1

As proved below.

Explanation:

`"To prove " sin 2x = (2tanx) / (1 + tan^2x)`

Let us start from R H S and prove it equal to L H S.

`R H S = (2tan x) / (1 + tan^2x)`

`=> (2 tan x) / sec^2 x, " as " 1 + tan^2x = sec^2x, "identity"`

`=> (2(sin x / cancelcos x)) / (1/cancel(cos^2x)^color(red)(cosx))`

`=> 2 sin x cos x = sin 2x` as per `sin 2x = 2 sin x cos x " identity"`

`=> L H S`