Fractional and surd forms of trigonometric ratios

In Figure 45.1, ABC is an equilateral triangle of side 2 units. AD bisects angle A and bisects the side BC. Using Pythagoras’ theorem on triangle ABD gives: Figure 45.1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/fig45_1.tif"/> AD = 2 2 − 1 2 = 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq1588.tif"/>