Difference between revisions of "2002 AMC 12P Problems/Problem 17"
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== Problem == | == Problem == | ||
| − | + | Let <math>f(x) = \sqrt{\sin^4{x} + 4 \cos^2{x}} - \sqrt{\cos^4{x} + 4 \sin^2{x}}.</math> An equivalent form of <math>f(x)</math> is | |
<math> | <math> | ||
| − | \text{(A) } | + | \text{(A) }1-\sqrt{2}\sin{x} |
\qquad | \qquad | ||
| − | \text{(B) } | + | \text{(B) }-1+\sqrt{2}\cos{x} |
\qquad | \qquad | ||
| − | \text{(C) } | + | \text{(C) }\cos{\frac{x}{2}} - \sin{\frac{x}{2}} |
\qquad | \qquad | ||
| − | \text{(D) } | + | \text{(D) }\cos{x} - \sin{x} |
\qquad | \qquad | ||
| − | \text{(E) } | + | \text{(E) }\cos{2x} |
</math> | </math> | ||
| + | |||
| + | [[2002 AMC 12P Problems/Problem 17|Solution]] | ||
== Solution == | == Solution == | ||
Revision as of 00:53, 30 December 2023
Problem
Let 
An equivalent form of 
is
Solution
If 
, then 
. Since 
, 
must be 
to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of 
.
See also
| 2002 AMC 12P (Problems • Answer Key • Resources) | |
| Preceded by Problem 16 |
Followed by Problem 18 |
| 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. 
