SOLUTION: Using the expression cos (75 degrees) cos (30 degrees) + sin (75 degrees) sin (30 degrees) a) write the expression as the cosine of an angle. b) find the exact value of the

Algebra ->  Trigonometry-basics -> SOLUTION: Using the expression cos (75 degrees) cos (30 degrees) + sin (75 degrees) sin (30 degrees) a) write the expression as the cosine of an angle. b) find the exact value of the      Log On


   

Question 912089: Using the expression cos (75 degrees) cos (30 degrees) + sin (75 degrees) sin (30 degrees)
a) write the expression as the cosine of an angle.
b) find the exact value of the expression
Can someone please help me with this problem, please? Im really stuck on hw and an example could help
thank you!
Found 2 solutions by Edwin McCravy, ewatrrr:
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
cos(75°)cos(30°)+sin(75°)sin(30°) 
(a)
Use the double angle identity:
cos%28alpha-beta%29=cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29

Observe that the given expression is the right side of this
identity with alpha=%2275%B0%22 and beta=%2230%B0%22, Substituting





Answer:  cos(45°)

(b) 
Since the exact vaule of cos(45°) is sqrt%282%29%2F2,

 cos(75°)cos(30°)+sin(75°)sin(30°) = sqrt%282%29%2F2

Edwin

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
cos (75 degrees) cos (30 degrees) + sin (75 degrees) sin (30 degrees)= cos(75-30) = cos(45)