1. 9-2: Addition and
Subtraction Identities
Learning Goals:
•Use the addition and
subtraction identities for sine,
cosine & tangent
©2009 Roy L. Gover (www.mrgover.com)

2. Review
Find the exact values:
1. sin 2. cos180
2
3. sin 4. sin 270
3
5. cos 6. cos
2 2
°
°
π
π
π π

3. Review
60°
30°
1
23 45°
45°
1
1
2

4. Review
1
23 1
1
2
π
6
π
3
π
4
π
4

5. Review
Find the exact values:
1. sin 30 2. tan
6
3. cos 45 4. sin
3
5
5. cos 6. tan220
4
°
°
°
π
π
π

6. Does cos 40°+
cos 10°=cos 50°?
Analysis
Inquiring Minds Want To
Know…

7. cos(α+β)=cosα cosβ-sinα sinβ
cos(α-β)=cosα cosβ+sinα sinβ
Addition & Subtraction
Identities for Cosine:
Important Idea
cos( )
cos cos sin sin
α β
α β α β
± =
m

8. Example
Find the exact value of
cos 75° using the values of
the function for 30° and
45°

9. Example
Find the exact value of
cos using the values
of the function for
and
π
3
π
4
7π
12
 
 ÷
 

10. Try This
Find the exact value of cos
15° using the values of the
function for 60° and 45°. Hint:
cos 15°=cos(60°-45°)
2 6
4 4
+

11. Try This
Find exact value of cos
using the values of the
function for and . Hint: cos
=
cos
2 6
4 4
+
π
12
 
 ÷
 
π
3
π
4π
12
 
 ÷
 
π π
3 4
 
− ÷
 

12. Example
Rewrite the given
expression in terms of sin x
and/or cos x: cos(x + )π

13. sin(α+β)=sinα cosβ+cosα sinβ
sin(α-β)=sinα cosβ - cosα sinβ
Addition & Subtraction
Identities for Sine:
Important Idea
sin( )
sin cos cos sin
α β
α β α β
± =
±

14. Example
Find the exact value of sin
75°. Simplify your answer.

15. Example
Find exact value of sin
Hint:
Simplify your answer.
13π
12
 
 ÷
 5π π 13π
4 6 12
 
− = ÷
 

16. Try This
Find exact value of sin
Hint:
5π
12
 
 ÷
 2π π 5π
3 4 12
 
− = ÷
 
Simplify your
answer.
6 2
4
+

17. Try This
Verify the identity:
sin(270°+x)=-cos x

18. Solution
sin(270 )
sin 270 cos cos270 sin
1(cos ) 0(sin )
cos
x
x x
x x
x
°+
= ° + °
= − +
= −

19. tan tan
tan( )
1 tan tan
α β
α β
α β
+
+ =
−
tan tan
tan( )
1 tan tan
α β
α β
α β
−
− =
+
Addition & Subtraction
Identities for Tangent…
Important Idea

20. tan tan
tan( )
1 tan tan
α β
α β
α β
±
± =
m
Addition & Subtraction
Identities for Tangent-the
condensed form:
Important Idea

21. Example
Find the exact value of tan
15° using the values of the
tan function for 45° and 30°.
Simplify your answer.

22. Try This
If sin A= & cos B= ,
find tan(A+B).
4
5
3
5
24
7
−

23. Lesson Close
Describe a method for
finding the exact value
of sin 105°.