SOLUTION: Compute     {{{ (sin13 + sin47 + sin73 + sin 107) / cos17 }}} (All numbers are in degrees)

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Question 1176720: Compute      (All numbers are in degrees)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


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Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
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Compute     .

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                    Solution


Let simplify the numerator,  step by step. 


(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(30°)*cos(17°) =  = 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.     ANSWER


Solved.



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