Answer 1

Given θ = 30°  ....(1)

To veriy

`sin 2theta = (2 tan theta)/(1 + tan^2 theta)` ....(2)

`sin 2 theta = sin 2 xx 30`

= sin 60

`= sqrt3/2`

Now consider right hand side

`(2 tan theta)/(1 + tan^2 theta) = (2 tan 30)/(1 + tan^2 30)`

`= (2 xx 1/sqrt3)/(1 + (1/sqrt3)^2)`

`= sqrt3/2`

Hence it is verified that,

`sin 2theta = (2 tan theta)/(1 + tan^2 theta)`