SOLUTION: Use a product-to-sum or sum-to-product identity to complete the simplification shown below. sin(36 degrees)+sin(24 degrees)=sin(A) where the exact value of A with 0 degrees <

Algebra ->  Trigonometry-basics -> SOLUTION: Use a product-to-sum or sum-to-product identity to complete the simplification shown below. sin(36 degrees)+sin(24 degrees)=sin(A) where the exact value of A with 0 degrees <      Log On


   

Question 827541: Use a product-to-sum or sum-to-product identity to complete the simplification shown below.
sin(36 degrees)+sin(24 degrees)=sin(A)
where the exact value of A with 0 degrees < A < 90 degrees is:
A =
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Use a product-to-sum or sum-to-product identity to complete the simplification shown below.
sin(36 degrees)+sin(24 degrees)=sin(A)
where the exact value of A with 0 degrees < A < 90 degrees is:
***
sin%28s%29%2Bsin%28t%29=2%28sin%28s%2Bt%29%2F2%29%28cos%28s-t%29%2F2%29=sin%28A%29
sin%2836%29%2Bsin%2824%29=2%28sin%2836%2B24%29%2F2%29%28cos%2836-24%29%2F2%29=sin%28A%29
sin%2836%29%2Bsin%2824%29=2sin%2830%29cos%286%29=sin%28A%29
sin%2836%29%2Bsin%2824%29=2%281%2F2%29cos%286%29=sin%28A%29
cos(6)=sin(A)
cos(6)=sin(90-6)=sin(84)
sin(A)=sin(84)
A=84˚
..
calculator check:
sin(36)+sin(24)≈0.9945..
sin(A)=sin84≈0.9945..