Question

sin(1/3arcsin1-arcsin4/5)

Answer 1

sin(1/3arcsin1-arcsin4/5)=sin(1/3*π/2-arcsin4/5)=sin(π/6-arcsin4/5)=sinπ/6cosarcsin4/5+cosπ/6sinarcsin4/5=1/2cosarcsin4/5+4√3/10=

=1/2*√(1-sin²(arcsin4/5))+2√3/5=1/2*3/5+4√3/10=(4√3+3)/10