How do you find the value of tan15 using the half angle?

1 Answer
Jun 24, 2016

tan(theta/2) = +-sqrt((1 - costheta)/(1 + costheta))

Since we are looking for tan15^@, theta = 30^@.

tan15^@ = +-sqrt((1 - sqrt(3)/2)/(1 + sqrt(3)/2))

tan15^@ = +-sqrt(((2 - sqrt(3))/2)/((2 + sqrt(3))/2))

tan15^@ = +-sqrt((2 - sqrt(3))/(2 + sqrt(3)

By calculator, this can be simplified to 2 - sqrt(3)

Since tangent is positive in quadrant 1, tan15^@ =2 - sqrt(3).

Hopefully this helps!