Question

How to find tan(22{1/2}) degrees ?

Answer 1

Solution:

22½° lies in the first quadrant.

Therefore, tan 22½° is positive.

For all positive values of the angle A we know that, tan A2 = √1−cosA1+cosA

tan 22½° = √1−cos45°1+cos45°

tan 22½° = √1−1√21+1√2, [Since we know that cos 45° = 1√2]

tan 22½° = √√2−1√2+1

tan 22½° = √√2−1√2+1⋅√2−1√2−1

tan 22½° = √(√2−1)22−1

tan 22½° = √2 - 1

Therefore, tan 22½° = √2 - 1