Question

`(1 - tan^2 30°)/(1 + tan^2 30°)` is equal to _________.

Options

• cos 60°

• sin 60°

• 1

• tan²60°

Answer 1

`(1 - tan^2 30°)/(1 + tan^2 30°)` is equal to cos 60°.

Explanation:

cos(60°) = `1/2`

tan(30°) = `1/sqrt3`

Taking L.H.S. = cos60° = `1/2`

Now, solving R.H.S.

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

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

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

= `2/4`

= `1/2`

∴ L.H.S. = R.H.S.

Hence proved.