SOLUTION: Solve: Arc sin 2x + Arc sin x = pi/2.

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Question 33173: Solve: Arc sin 2x + Arc sin x = pi/2.
Answer by Fermat(136) About Me  (Show Source):
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Let A = asin(2x)
Let B = asin(x)
then
A + B = pi/2
cos(A+B) = cos(pi/2)
cosAcosB - sinAsinB = 0
cosAcosB - (2x)(x) = 0
cosAcosB = 2x²
cos²Acos²B = 4x^4
(1-sin²A)(1-sin²B) = 4x^4
(1-4x²)(1-x²) = 4x^4
1 - x² - 4x² + 4x^4 = 4x^4
1 - 5x² = 0
5x² = 1
x = 1/sqrt(5)
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