SOLUTION: Compute {{{ (sin13+sin47+sin73+sin107)/(cos17) }}}. (In degrees)

Algebra ->  Trigonometry-basics -> SOLUTION: Compute {{{ (sin13+sin47+sin73+sin107)/(cos17) }}}. (In degrees)      Log On


   

Question 1113579: Compute +%28sin13%2Bsin47%2Bsin73%2Bsin107%29%2F%28cos17%29+. (In degrees)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


13 = 30-17; 47 = 30+17.

sin%2830-x%29%2Bsin%2830%2Bx%29
= %28sin30cosx-cos30sinx%29%2B%28sin30cosx%2Bcos30sinx%29
= 2sin30cosx
= cosx

So
sin13%2Bsin47+=+cos17

73 = 90-17; 107 = 90+17.

sin%2890-x%29%2Bsin%2890%2Bx%29
= %28sin90cosx-cos90sinx%29%2B%28sin90cosx%2Bcos90sinx%29
= 2sin90cosx
= 2cosx

So
sin73%2Bsin107+=+2cos17

And so then
sin13%2Bsin47%2Bsin73%2Bsin107+=+3cos17

And finally
%28sin13%2Bsin47%2Bsin73%2Bsin107%29%2Fcos17+=+3