If tan pi8 Squareroot A B then by using a half angle form

If tan pi/8 = Squareroot A - B, then, by using a half - angle formula, find A =, B = .

Solution

Solution:

Given tan(pi/8) = Sqrt(A) - B .....................(1)

tan(pi/8) = sin(pi/8) / cos(pi/8)
            = 2sin(pi/8)cos(pi/8) / 2 cos^2(pi/8)
            = sin(pi/4) / [1 + cos(pi/4)]
            = [1/sqrt(2)] / [1 + 1/sqrt(2)]
            = 1 / [sqrt(2) + 1]

multiply and divide by (sqrt(2) - 1)

          = (sqrt(2) - 1) / (sqrt(2) + 1) (sqrt(2) - 1)

          = (sqrt(2) - 1) / (2 - 1)

          = (sqrt(2) - 1)    ................................................(2)

Compare (1) and (2);

A = 2 and B = 1