Download Sum and Difference Identities

Pre-Calculus
Lesson 23: Sum & Difference Identities
Name: ___________________________
Date: _____________
Period: 1 2 3 4 5 6 7 8
Take a look at the problems to the right. How would you do these without a calculator?
cos75
sin
Sum and Difference Identities
sin  A  B   sin A cos B  cos A sin B
cos  A  B   cos A cos B  sin A sin B
sin  A  B   sin A cos B  cos A sin B
cos  A  B   cos A cos B  sin A sin B
tan  A  B  
tan A  tan B
1  tan A tan B
tan  A  B  
tan A  tan B
1  tan A tan B
Examples
Find the EXACT values of the following using the Sum and Difference Identities.
1. cos75
2.
sin
3.
tan

12
13
12
Use an addition or subtraction identity to write the expression as a trigonometric function of one angle. Then, find the
exact value of the expression.
4. sin80 cos 20  cos80 sin 20


 sin
5.
cos
6.
tan135  tan 45
1  tan135 tan 45
9
cos
18

9
sin

18

12
Pre-Calculus
Lesson 23: Sum & Difference Identities
Verify the following identities using the Sum and Difference Identities.


7. cos   x   sin x
 2

8.
 

sin  x    cos x
2 

9.
1  tan x


 tan   x 
1  tan x
 4

Name: ___________________________
Date: _____________
Period: 1 2 3 4 5 6 7 8