Question

Solve the equation:

arcsin x · arccos x = π²/16

I want the demonstration to be complete. Thanks

Answer 1

x = √2/2

Explanation:

Use the identity:

arcsin x + arccos x = π/2

Therefore, we can rewrite this as:

arcsin x (π/2 − arcsin x) = π²/16

If we substitute y = arcsin x:

y (π/2 − y) = π²/16

π/2 y − y² = π²/16

0 = y² − π/2 y + π²/16

0 = 16y² − 8π y + π²

0 = (4y − π)²

y = π/4

Substituting back:

arcsin x = π/4

x = sin(π/4)

x = √2/2