SOLUTION: If sin^2(π/9) + sin^2(2π/9) + sin^2(3π/9) + sin^2(4π/9) = 9/4 , evaluate cos^2(π/9) + cos^2(2π/9) + cos^2(3π/9) + cos^2(4π/9).

Algebra ->  Trigonometry-basics -> SOLUTION: If sin^2(π/9) + sin^2(2π/9) + sin^2(3π/9) + sin^2(4π/9) = 9/4 , evaluate cos^2(π/9) + cos^2(2π/9) + cos^2(3π/9) + cos^2(4π/9).      Log On


   

Question 523797: If sin^2(π/9) + sin^2(2π/9) + sin^2(3π/9) + sin^2(4π/9) = 9/4 , evaluate
cos^2(π/9) + cos^2(2π/9) + cos^2(3π/9) + cos^2(4π/9).
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's 1.75.
The 1st line, "if..." is not needed.
As a check,
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sin^2(pi/9) + sin^2(2pi/9) + sin^2(3pi/9) + sin^2(4pi/9) = 9/4
cos^2(pi/9) + cos^2(2pi/9) + cos^2(3pi/9) + cos^2(4pi/9) = x
---------------------------------------------------------------- Add
1 + 1 + 1 + 1 = x + 9/4
x = 7/4