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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

From the quotient relation and the above formulae,

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