2006 AIME I Problems/Problem 12
Problem
Find the sum of the values of such that , where is measured in degrees and
Solution
Using the sum and difference formulas for the cosine function:
Expanding the expression:
Combining like terms:
Factoring :
Using the difference of squares factorization:
Using the sum and difference formulas for cosine in reverse:
Setting each non-constant factor equal to 0:
So the sum of the values of where is:
See also
2006 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |