Question 1156524
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Use the identities for sin(A+B) and sin(A-B) and simplify....<br>
{{{(sin(18) + sin(42) + sin(78) + sin (102)) / cos(12)}}}<br>
{{{(sin(30-12) + sin(30+12) + sin(90-12) + sin (90+12)) / cos(12)}}}<br>
{{{(sin(30)cos(12)-cos(30)sin(12) + sin(30)cos(12)+cos(30)sin(12) + sin(90)cos(12)-cos(90)sin(12) + sin(90)cos(12)+cos(90)sin(12))/cos(12)}}}<br>
{{{(2*sin(30)cos(12)+2(sin(90)cos(12)))/cos(12)}}}<br>
{{{2sin(30)+2sin(90) = 2(1/2)+2(1) = 1+2 = 3}}}<br>
ANSWER: 3<br>