Question

Without using tables, evaluate the following: tan²30° + tan²60° + tan²45°

Answer 1

tan²30° + tan²60° + tan²45°

tan30° = `(1)/sqrt(3)`

tan60° = `sqrt(3)`
tan45° = 1
tan²30° + tan²60° + tan²45°

= `(1/sqrt(3))^2 + (sqrt(3))^2 + 1`

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

= `(1 + 9 + 3)/(3)`

= `(13)/(3)`.