Question 1177720
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Compute     {{{ (sin(13^o) + sin(47^o) + sin(73^0) + sin(107^o) )/ cos(17^o) }}}.


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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Solution</U>



Let simplify the numerator, &nbsp;step by step.



<pre>
(1)  sin(73°) = cos(90° - 73°) = cos(17°).


     sin(107°) = sin(73°) = cos(17°)


     So, the sum of the third and the fourth terms in the numerator is  2*cos(17°).




(2)  sin(13°) + sin(47°) = ( use the basic formuls of trigonometry sin(a) + sin(b) = {{{2*sin((a+b)/2)*cos((a-b)/2)}}} ) = 

                         = 2*sin(30°)*cos(17°) = {{{2*(1/2)*cos(17^o)}}} = cos(17°)


     THEREFORE, the sum of four terms in the numerator is  3*cos(17°).




(3)  Then it becomes OBVIOUS that the entire fraction is  equal to 3.     <U>ANSWER</U>
</pre>


Solved.