# How do you use the half angle identity to find exact value of tan 67.5?

##### 1 Answer

Nov 14, 2015

Find tan (67.5)

Ans: (1 + sqrt2)

#### Explanation:

Call tan (67.5) = tan x --> tan 2x = (tan 135^@) = -1

Apply the trig identity:

We get:

Solve the quadratic equation in tan x:

Since the arc (67.5) is in Quadrant I, then its tan is positive.

Check by calculator.

tan (67.5) = 2.41