∠XAB =
90- (OAB
is a
right angle, and XAB is 90°-α)
So angle ABX=α (triangle XAB is a right angled triangle, so
ABX=90°-(90°-α)=α)
Also, ∠OBA in triangle ABO is (90°-β), so
angle
OAB=90°-α-β
Angles of interest are marked on the diagram (Fig 1).
Proof
of the Sine and Cosine Compound Angles
Proof
of sin(α+β)=sinα cosβ
+cosα sineβ
We wish to prove that:
Or perhaps discover a relationship for the angle sum less than
π/2