SOLUTION: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)

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Question 867653: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)
Answer by Edwin McCravy(20062) (Show Source):
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sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�) = Put some terms in the middle: sin�(1�)+sin�(2�)+��+sin�(44�)+sin�(45�)+sin�(46�)+��+sin�(88�)+sin�(89�) sin�(1�)+sin�(2�)+��+sin�(44�)+sin�(45�)+sin�(90�-44�)+��+sin�(90�-2�)+sin�(90�-1�) Use the fact that sin(90�-q) = cos(q) sin�(1�)+sin�(2�)+��+sin�(44�)+sin�(45�)+cos�(44�)+��+cos�(2�)+cos�(1�) = Rearrange the terms putting the 1st and 89th terms together, 2nd and 88th terms together, �� 44th and 46th terms together: [sin�(1�)+cos�(1�)]+[sin�(2�)+cos�(2�)]+��+[sin�(44�)+cos�(44�)]+sin�(45�) = Use the fact that sin�(q)+cos�(q) = 1 1 + 1 + �� + 1 + sin�(45�), where there are 44 1's. 44 + sin�(45�) = 44 + = 44 + = 44 + = 44.5 Edwin

SOLUTION: sin�(1�)+sin�(2�)+���+sin�(88�)+sin�(89�)

SOLUTION: sin�(1�)+sin�(2�)+��+sin�(88�)+sin�(89�)