Question

If 𝜃 = 30° verify `cos 2 theta = (1 - tan^2 theta)/(1 + tan^2 theta)`

Answer 1

Given 𝜃 = 30° ........(1)

To verify

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

Now consider left hand side of the equation (2)

Therefore

`cos 2 theta = cos 2 xx 30`

= cos 60

`= 1/2`

Now consider right hand side of equation (2)

Therefore

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

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

`= (1 - 1/3)/(1 + 1/3)`

`= 1/2`

Hence it is verified that,

`cos 2 theta = (1 - tan^2 theta)/(1 + tan^2 theta)`