Arc sin 2x + arc sin x = pi/2

Question

Arc sin 2x + arc sin x = pi/2

Answer 1

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)Let B = asin(x)
then
A + B = pi/2
cos(A+B) = cos(pi/2)
cosAcosB - sinAsinB = 0
cosAcosB - (2x)(x) = 0
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