Sum and difference formulas

sin (x + y) = sin x . cos y + cos x . sin y
sin (x – y) = sin x . cos y – cos x . sin y
cos (x + y) = cos x . cos y – sin x . sin y
cos (x – y) = cos x . cos y + sin x . sin y

1.Simplify:

Solution:

2.Calculate:

Solution:

3.Prove identity:

4.Prive identity when:  :

Solution:

Identity is valid when:

5.Write formulas for the sum and difference of trigonometric functions:

Solution:

Solution:

7. Prove that it applies, when:

Solution:

Identity valid.

8.Prove that it applies:

Solution:

Identity valid when: (x – y) ≠ (2k + 1)π