Question

Find the exact value of tan 22.5.

Answer 1

Use the half-angle identity

tan(x/2) = ±sin(x)) / (1 + cos(x))

The angle is in the first quadrant, so its tangent is positive.

sin(45°) = cos(45°) = √2 / 2

If you rationalize the denominator and simplify the result, you should get

√2 - 1