Difference between revisions of "2012 AIME II Problems/Problem 9"
Williamhu888 (talk | contribs) (Created page with "== Problem 9 == Let <math>x</math> and <math>y</math> be real numbers such that <math>\frac{\sin x}{\sin y} = 3</math> and <math>\frac{\cos x}{\cos y} = \frac12</math>. The value...") |
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== Problem 9 == | == Problem 9 == | ||
Let <math>x</math> and <math>y</math> be real numbers such that <math>\frac{\sin x}{\sin y} = 3</math> and <math>\frac{\cos x}{\cos y} = \frac12</math>. The value of <math>\frac{\sin 2x}{\sin 2y} + \frac{\cos 2x}{\cos 2y}</math> can be expressed in the form <math>\frac pq</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | Let <math>x</math> and <math>y</math> be real numbers such that <math>\frac{\sin x}{\sin y} = 3</math> and <math>\frac{\cos x}{\cos y} = \frac12</math>. The value of <math>\frac{\sin 2x}{\sin 2y} + \frac{\cos 2x}{\cos 2y}</math> can be expressed in the form <math>\frac pq</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>. | ||
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| + | == Solution == | ||
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| + | == See also == | ||
| + | {{AIME box|year=2012|n=II|num-b=8|num-a=10}} | ||
Revision as of 16:21, 31 March 2012
Problem 9
Let 
and 
be real numbers such that 
and 
. The value of 
can be expressed in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See also
| 2012 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
