Question

tan² 30° − tan² 45° + tan² 60°

Options

• `2 1/3`

• `8 1/3`

• `−3 2/3`

• 0

Answer 1

`bb2 bb1/bb3`

Explanation:

tan 30° = `1/sqrt3 = tan^2 30° = 1/3`

tan⁡ 45∘ = 1 ⇒ tan⁡² 45∘ = 1

tan 60^∘ = `sqrt3 = tan^2 60° = 3`

`tan^2 30° − tan^2 45° + tan^2 60°  = 1/3 − 1 + 3 = (− 2/3 + 3) = 7/3`

`7/3 = 2 1/3`