Difference between revisions of "2002 AMC 12P Problems/Problem 10"
The 76923th (talk | contribs) (→Solution) |
The 76923th (talk | contribs) (→Solution) |
||
Line 19: | Line 19: | ||
Divide by 2 on both sides to get <cmath>3f_{4}(x)-2f_{6}(x)=f_{2}(x)?</cmath> | Divide by 2 on both sides to get <cmath>3f_{4}(x)-2f_{6}(x)=f_{2}(x)?</cmath> | ||
Substituting the definitions of <math>f_{2}(x)</math>, <math>f_{4}(x)</math>, and <math>f_{6}(x)</math>, we may rewrite the expression as | Substituting the definitions of <math>f_{2}(x)</math>, <math>f_{4}(x)</math>, and <math>f_{6}(x)</math>, we may rewrite the expression as | ||
− | <cmath>3(\text{sin}^4 x + \text{cos}^4 x)</cmath> | + | <cmath>3(\text{sin}^4 x + \text{cos}^4 x) - 2(\text{sin}^6 x + \text{cos}^6 x) = 1</cmath> |
== See also == | == See also == | ||
{{AMC12 box|year=2002|ab=P|num-b=9|num-a=11}} | {{AMC12 box|year=2002|ab=P|num-b=9|num-a=11}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 11:48, 10 March 2024
Problem
Let For how many in is it true that
Solution
Divide by 2 on both sides to get Substituting the definitions of , , and , we may rewrite the expression as
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.