Log256sin5П/8+log256si6П/8+log256sin7П/8

Question

Log256sin5П/8+log256si6П/8+log256sin7П/8

Answer 1

Sin5π/8=cos(-π/8)=cosπ/8
sin6π/8=sinπ/4
sin7π/8=sinπ/8
log(256)(cosπ/8*sinπ/4*sinπ/8)=log(256)(1/2*sinπ/4*sinπ/4)=
=log(256)(1/2*sin²π/4)=log(256)(1/2*1/2)=log(256)1/4=-1/4