5.4 Sum and Difference Formulas
Sum and Difference Formulas
sin  u  v   sin u cos v  cos u sin v
sin  u  v   sin u cos v  cos u sin v
cos  u  v   cos u cos v  sin u sin v
cos  u  v   cos u cos v  sin u sin v
tan u  tan v
1  tan u tan v
tan u  tan v
tan  u  v  
1  tan u tan v
tan  u  v  
Examples: Find the exact value of each expression.
  
 
4 3
1. cos 
2. sin(135 30 )
Examples: Find the exact values of the sine, cosine, and tangent of the angle.
1.
11 3 


12
4 6
2. 
17
12
3. 105
Examples: Write the expression as the sine, cosine, or tangent of an angle.
1. sin 3cos1.2  cos3sin1.2
2.
3.
Examples: Find the exact value of the trig function given that sin u 
are in quadrant II.
1. cos  u  v 
2. sin  u  v 
3. sec  v  u 
Examples: Prove the identity.


 x   cos x
2

1. sin 
5
3
and cos v   . Both u and v
13
5
2
 5

 x  
 cos x  sin x 
2
 4

2. cos 
Examples: Find all solutions in [0,2π).
1. sin  x     sin x  1  0
2. tan  x     2sin  x     0