CHAPTER 4: TRIGONOMETRIC ADDITION
FORMULAE
Addition formulae
Example 1: Prove that
cos 𝐴 sin 𝐴 cos(𝐴 + 𝐵)
− =
sin 𝐵 cos 𝐵 sin 𝐵 cos 𝐵
s nA RHS
uts
Example 2:
Ist
Given that 2 sin(𝑥 + 𝑦) = 3 cos(𝑥 − 𝑦), express tan 𝑥 in terms of tan 𝑦.
25in g 30s x y
2 sinxcosy singcos 3 cosxcosy Sinxsing
CosxCosy 3 3 Sinxsing
2 SinxCosy ZsingCosx
3 cos Cosy 2singCOSX
2SinxCosy 3sinxSiny
2sing
Sinx 2Cosy sing
3 Cost rosy
t.mx s i I I
III
, Example 3:
√ √
Show, using the formula for sin(𝐴 − 𝐵), that sin 15° =
450 3007
sin A B Sin
Sint56530 costs sin 30
E LES CE
6
E E
Example 4: B 480
98
COSACosB sin AsinB 3 53 33
A COCA B
We have tofind cos and SinB
CORB SIRB 1
I Is c 7 sin B
EET
COSA 1 132 SiñB
COSA
Is sinB g
A
a s si sink
tan At B
tan A
tanB 3,5 2
a cosecia
if
FORMULAE
Addition formulae
Example 1: Prove that
cos 𝐴 sin 𝐴 cos(𝐴 + 𝐵)
− =
sin 𝐵 cos 𝐵 sin 𝐵 cos 𝐵
s nA RHS
uts
Example 2:
Ist
Given that 2 sin(𝑥 + 𝑦) = 3 cos(𝑥 − 𝑦), express tan 𝑥 in terms of tan 𝑦.
25in g 30s x y
2 sinxcosy singcos 3 cosxcosy Sinxsing
CosxCosy 3 3 Sinxsing
2 SinxCosy ZsingCosx
3 cos Cosy 2singCOSX
2SinxCosy 3sinxSiny
2sing
Sinx 2Cosy sing
3 Cost rosy
t.mx s i I I
III
, Example 3:
√ √
Show, using the formula for sin(𝐴 − 𝐵), that sin 15° =
450 3007
sin A B Sin
Sint56530 costs sin 30
E LES CE
6
E E
Example 4: B 480
98
COSACosB sin AsinB 3 53 33
A COCA B
We have tofind cos and SinB
CORB SIRB 1
I Is c 7 sin B
EET
COSA 1 132 SiñB
COSA
Is sinB g
A
a s si sink
tan At B
tan A
tanB 3,5 2
a cosecia
if
