SOLUTION: Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. cos(70°)cos(20°)-sin(70°)sin(20°)

Algebra ->  Expressions -> SOLUTION: Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. cos(70°)cos(20°)-sin(70°)sin(20°)      Log On


   

Question 518475: Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.
cos(70°)cos(20°)-sin(70°)sin(20°)
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity

  cos%28alpha%2Bbeta%29 ≡ cos%28alpha%29cos%28beta%29 - sin%28alpha%29sin%28beta%29

Substitute alpha = 70°, beta = 20°

cos%28%2270%B0%22%2B%2220%B0%22%29 ≡ cos%28%2270%B0%22%29cos%28%2220%B0%22%29 - sin%28%2270%B0%22%29sin%28%2220%B0%22%29

   cos%28%2290%B0%22%29 ≡ cos%28%2270%B0%22%29cos%28%2220%B0%22%29 - sin%28%2270%B0%22%29sin%28%2220%B0%22%29

       0 ≡ cos%28%2270%B0%22%29cos%28%2220%B0%22%29 - sin%28%2270%B0%22%29sin%28%2220%B0%22%29

So the answer is 0.

Edwin