In the diagram BAC = , CAF = and AC = 1. Additionally lines

In the diagram ∠BAC = β, ∠CAF = α − β and AC = 1. Additionally lines AB and BC are perpendicular.

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a Show each of the following: LFAB=a i iii AB = cos 3 ii ZABD = a and ZECB = a iv BC = sin 3 b Use AABD to write an expression for the lengths i AD ii BD c Use ABEC to write an expression for the lengths i CE ii BE d Use AFAC to write an expression for the lengths i FC ii FA e Use your completed diagram to show that: i sin (a 3) = sin a cos 3- cos a sin 3 cos (a -3) = cos a cos 3 + sin a sin 3 ii