1. COMPOUND ANGLE FORMULAE: sin(A + B)
Draw a horizontal base line.

2. COMPOUND ANGLE FORMULAE: sin(A + B)
Add a second line at an angle to the first.
Label this angle A A

3. COMPOUND ANGLE FORMULAE: sin(A + B)
Label this angle B
Add a third line above the second. B A

4. COMPOUND ANGLE FORMULAE: sin(A + B)T Q
Call this point O B A O R P

5. COMPOUND ANGLE FORMULAE: sin(A + B)
Can you identify all the equal angles? T Q B A O R P

6. COMPOUND ANGLE FORMULAE: sin(A + B)
Those marked
equal (90 – A)o T Q B A O R P

7. COMPOUND ANGLE FORMULAE: sin(A + B)
These angles are equal to angle A A
90 – A T Q B A A O R P

8. COMPOUND ANGLE FORMULAE: sin(A + B)T S R Q P O
90 – A B A T S R Q P O
90 – A

9. COMPOUND ANGLE FORMULAE: sin(A + B)T Q B A O R P

10. COMPOUND ANGLE FORMULAE: sin(A + B)
we can rewrite this
90 – A A
as.. T Q B A O R P
from this

11. COMPOUND ANGLE FORMULAE: sin(A + B)
Continuing….
Rearrange… S
sin(A + B)
90 – A A T Q B A O R P

12. COMPOUND ANGLE FORMULAE: sin(A + B)
In conclusion:
sin(A + B)

13. If we replace B by (-B) in formula of sin(A – B), we have

14. If we replace A by (/2 - A) in the formula of sin(A - B), we have

15. By substituting (- B) in the formula of cos(A + B), we have

16. From the quotient relation and the above formulae,

17. By substituting (-B) for B in the formula tan(A + B)