document.write( "Question 1177720: What is the value of (sin 13° + sin 47° + sin 73° + sin 107°)/(cos 17°)? \n" ); document.write( "

Algebra.Com's Answer #806824 by ikleyn(52805) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Let simplify the numerator, step by step.\r
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document.write( "(1)  sin(73°) = cos(90° - 73°) = cos(17°).\r\n" );
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document.write( "     sin(107°) = sin(73°) = cos(17°)\r\n" );
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document.write( "     So, the sum of the third and the fourth terms in the numerator is  2*cos(17°).\r\n" );
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document.write( "(2)  sin(13°) + sin(47°) = ( use the basic formuls of trigonometry sin(a) + sin(b) =  ) = \r\n" );
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document.write( "                         = 2*sin(30°)*cos(17°) =  = cos(17°)\r\n" );
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document.write( "     THEREFORE, the sum of four terms in the numerator is  3*cos(17°).\r\n" );
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document.write( "(3)  Then it becomes OBVIOUS that the entire fraction is  equal to 3.     ANSWER\r\n" );
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