2002 AMC 12P Problems/Problem 17
Problem
Let An equivalent form of is
Solution 1
By the Pythagorean identity we can rewrite the given expression as follows.
Expanding each bracket gives
The expressions under the square roots can be factored to get
Since and for all real , the expression must evaluate to , which simplifies to .
Solution 2 (Cheese)
We don't actually have to solve the question. Just let equal some easy value to calculate and For this solution, let This means that the expression in the problem will give Plugging in for the rest of the expressions, we get
Therefore, our answer is .
Comment: If you decide to cheese the problem, be very careful not to choose any where is a multiple of . It turns out that all of them except for $\frac{7\pi}{4} + 2\pik$ (Error compiling LaTeX. Unknown error_msg) result in equality between the correct answer and one or more wrong answers.
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 |
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