Question

Evaluate and simplify tan 15º.

Answer 1

tan(15) = tan(45 - 30)

= [tan(45) - tan(30) ] / [ 1 + tan(30)tan(45)]

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

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

= (sqrt(3) - 1)^2 /(3 - 1)

= 1/2 [3 + 1 - 2sqrt(3) ]

= (2 - sqrt(3) )

= 0.27 is your answer