Difference between revisions of "2002 AMC 12P Problems/Problem 25"
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get <math>\sin{a}\cos{a} + \sin{b} \cos{b} = 0 </math> as <math> \sin^{2}{a}+\cos^{2}{a} = 1</math> and <math> \sin^{2}{b}+\cos^{2}{b} = 1</math>. | get <math>\sin{a}\cos{a} + \sin{b} \cos{b} = 0 </math> as <math> \sin^{2}{a}+\cos^{2}{a} = 1</math> and <math> \sin^{2}{b}+\cos^{2}{b} = 1</math>. | ||
− | So <math>\sin{(a+b)} = \frac{\sqrt{3}}{2} \Longrightarrow \boxed{\ | + | So <math>\sin{(a+b)} = \frac{\sqrt{3}}{2} \Longrightarrow \boxed{\textbf{(C) }\frac{\sqrt{3}}{2}}</math> |
Comment: This problem is pretty much identical to [[2007 AMC 12A Problems/Problem 17|2007 AMC 12A Problem 17]] except with different numbers. | Comment: This problem is pretty much identical to [[2007 AMC 12A Problems/Problem 17|2007 AMC 12A Problem 17]] except with different numbers. |
Latest revision as of 17:53, 15 July 2024
Problem
Let and
be real numbers such that
and
Find
Solution
Given
We multiply both sides of the syetem,
, then we get
. i.e.
.
We must get the sum of the first part of the equation, then we calculate , we will
get
as
and
.
So
Comment: This problem is pretty much identical to 2007 AMC 12A Problem 17 except with different numbers.
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 24 |
Followed by Last question |
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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