[Sin^-1 ({ √(4-d²) } /2)] - [d{ √(4-d²) } /4] = π/4
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[Sin^-1 ({ √(4-d²) } /2)] - [d{ √(4-d²) } /4] = π/4

[From: ] [author: ] [Date: 11-05-18] [Hit: ]
d ≈ 0.8079455066,d ≈ -1.829542035,......
It's hard to follow all of the various brackets and parentheses. But, if I'm reading it correctly, there is a numerical answer.

Put x = d/2 and y = √(4 - d²)/2. Then x² + y² = 1, and the equation reduces to a more manageable form.

arcsin(y) - y√(1 - y²) = π/4, if d > 0 or

arcsin(y) + y√(1 - y²) = π/4, if d < 0.

The equations have the solutions (obtained numerically)

y ≈ 0.914771017573, d > 0 and y ≈ 0.40397275330, d < 0.

Plugging these into the equation 2y = √(4 - d²) produces the solutions

d ≈ 0.8079455066, if d > 0

d ≈ -1.829542035, if d < 0.
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keywords: sup,radic,Sin,pi,[Sin^-1 ({ √(4-d²) } /2)] - [d{ √(4-d²) } /4] = π/4
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