Question 1113579
<br>
13 = 30-17; 47 = 30+17.<br>
{{{sin(30-x)+sin(30+x)}}}
= {{{(sin30cosx-cos30sinx)+(sin30cosx+cos30sinx)}}}
= {{{2sin30cosx}}}
= {{{cosx}}}<br>
So
{{{sin13+sin47 = cos17}}}<br>
73 = 90-17; 107 = 90+17.<br>
{{{sin(90-x)+sin(90+x)}}}
= {{{(sin90cosx-cos90sinx)+(sin90cosx+cos90sinx)}}}
= {{{2sin90cosx}}}
= {{{2cosx}}}<br>
So
{{{sin73+sin107 = 2cos17}}}<br>
And so then
{{{sin13+sin47+sin73+sin107 = 3cos17}}}<br>
And finally
{{{(sin13+sin47+sin73+sin107)/cos17 = 3}}}