Question

How do you write `tan(2x)` in terms of sinx?

Answer 1

`tan 2x = ((2sin x)/(1 - 2sin^2 x))sqrt(1 - sin ^2 x)`

Explanation:

`sin 2x = (sin 2x)/(cos 2x)`
Applying the 3 trig identities:
sin 2x = 2sin x.cos x , and
`cos 2x = (1 - 2sin^2 x)`
`cos x = sqrt(1 - sin^2 x)`
We get:
`tan 2x = (2sin x.cos x)/(1 - 2sin^2 x) =`
`= ((2sin x)/(1 - 2sin^2 x))sqrt(1 - sin^2 x)`