已知π/4
1个回答

存在公式arcsin(sinx)=x,它的成立条件是-π/2≤x≤π/2.

则arcsin[(sinx+cosx)/根号2]

=arcsin [sin(x+π/4)]

=arcsin [sin(π-x-π/4)]

=-arcsin[sin(x-3π/4)]------(此时x-3π/4在[-π/2,π/2]内)

=-(x-3π/4)

=3π/4-x