Question

How do you prove `(2tanx)/ (1+tan^2 x) = sin 2x`?

Answer 1

Please see below.

Explanation:

`(2tanx)/(1+tan^2x)`

= `(2sinx/cosx)/sec^2x`

= `(2sinx/cosx)/(1/cos^2x)`

= `(2sinx)/cosx xx cos^2x/1`

= `2sinxcosx`

= `sin2x`