Question

Evaluate the following

tan² 30° + tan² 60° + tan² 45°

Answer 1

tan² 30° + tan² 60° + tan² 45°  ....(i)

By trigonometric ratios we have

`tan 30^@ = 1/sqrt3       tan 60^@ = sqrt3         tan 45^@ = 1`

By substituting above values in (i), we get

`[1/sqrt3]^2 + [sqrt3]^2 + [1]^2`

`=> 1/3  + 3 + 1 => 1/3 + 4`

`=> (1 + 12)/3 = 13/3`