1. Sum and Difference Formulas

2. Does sin (π + π/2) = sin π + sin π/2 ?
No, -1 ≠ 1.
In general sin (a + b) ≠ sin a + sin b
But we have developed formulas to simplify many expressions.

3. a) sin (a + b) = sin a cos b + cos a sin b
b) sin (a – b) = sin a cos b – cos a sin b
c) cos (a + b) = cos a cos b – sin a sin b
d) cos (a – b) = cos a cos b + sin a sin b
e) tan (a + b) = tan a + tan b
1 - tan a tan b
f) tan (a - b) = tan a - tan b
1 + tan a tan b

4. We will first prove part d.

5. Simplify cos 2θ cos θ + sin 2θ sin θ
Show why cos (π/2 – θ) = sin θ
Find the exact value of cos 15°
Find the exact value of sin 42° cos 12 °– cos 42 °sin 12°

6. Now let’s prove part c.

7. If the sin s = 3/5 and sin t = -5/13, compute sin (s-t).
(s is in quadrant I and t is in quadrant III).

8. Prove part e.

9. a) Simplify tangent π/12.
b) Simplify tan π/9 + tan 2π/9
1 – tan π/9 tan 2π/9