Question

Find the value of tan 15°.

Answer 1

tan 15° = tan (45° - 30°)

`= (tan 45^circ - tan 30^circ)/(1 + tan 45^circ  tan 30^circ)`

`[because tan ("A - B") = (tan "A" - tan "B")/(1 + tan "A" tan "B")]`

`= (1 - 1/sqrt3)/(1 + 1 (1)/sqrt3)`

`= ((sqrt3- 1)/sqrt3)/((sqrt3 + 1)/sqrt3)`

`= (sqrt3 - 1)/cancel(sqrt3) xx cancel(sqrt3)/(sqrt3 + 1)`

`= (sqrt3 - 1)/(sqrt3 + 1) xx (sqrt3 - 1)/(sqrt3 - 1)`

`= (3 + 1 - 2sqrt3)/(3 - 1)`

`= (4 - 2sqrt3)/2`

`= 2 - sqrt3`