One of the chief appeals of Trigonometry to the beginner lies in the practical nature of the subject. The first aim in this respect is to obtain the formulae for the solution of the general triangle, but hitherto there has been much delay in the logical development of the subject up to that stage because of the need

(a) to prove the half-angle formula cos A =cos2 ½A − sin2 ½A and

(b) to show that cos (180° − A) = −cos A and sin(180°−A)= sin A.