proof trigonometric ratios for sum and difference of angles

Proof 1 - Using the Unit Circle

We will prove the cosine of the sum of two angles identity first, and then show that this result can be extended to all the other identities given.

cos (α + β) = cos α cos β − sin α sin β

We draw a circle with radius 1 unit, with point P on the circumference at (1, 0).

We draw an angle α from the centre with terminal point Q at (cos α, sin α), as shown. [Q is (cos α, sin α) because the hypotenuse is 1 unit.] learn more