Answer:
x = √2/2
Step-by-step 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
