Fun with Trigonometry

imageTrigonometry dates back to the ancient Greek astronomer/mathematicians and has been studied for centuries by students all over the world. If like me your experiences of the subject go back to the middle of the last century and the finer points are still somewhat shrouded in mystery - take up this nostalgic challenge and brush up with these basic exercises.

Derive from first principles the formulae for the Sine, Cosine, and Tangent of compound angles (select the appropriate link):-

a)    Sin(A + B) = SinA CosB + CosA SinB

b)    Sin(A - B) = SinA CosB - CosA SinB

c)    Cos(A + B) = CosA CosB - SinA SinB

d)    Cos(A - B) = CosA CosB + SinA SinB

e)    Tan (A + B) = TanA + TanB
                         1 - TanA TanB

f)     Tan (A - B) = TanA - TanB
                        1 + TanA TanB