Question

Find the value of:

2 tan² 30° − tan² 45° + tan² 60°

Answer 1

Given:

2 tan² 30° − tan² 45° + tan² 60°

Step 1: Use standard trigonometric values

tan 30° = `1/sqrt3 → tan^2 30° = 1/3`

tan 45° = 1 → `tan^2 45° = 1`

tan 60° = `sqrt3 → tan^2 60° = 3`

`2 ⋅ 1/3 − 1 + 3 = 2/3 − 1 + 3 = 8/3`

= `8/3 or 2 2/3`