SOLUTION: without using calculator, show that sin^2 30 degree + sin^2 45 degree + sin^2 60 degree = 3/2

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Question 632112: without using calculator, show that sin^2 30 degree + sin^2 45 degree + sin^2 60 degree = 3/2
Answer by Alan3354(69443) About Me  (Show Source):
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without using calculator, show that sin^2 30 degree + sin^2 45 degree + sin^2 60 degree = 3/2
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sin^2 30 degree + sin^2 45 degree + sin^2 60 degree = 3/2
cos(60) = sin(30)
sin^2 30 degree + sin^2 45 degree + cos^2 30 degree = 3/2
Sin^2(30) + cos^2(30) = 1
sin^2(45) + 1 = 3/2
sin(45) = sqrt(2)/2
sin^2(45) = 1/2
1 + 1/2 = 3/2