已知cos(a+π/4)=1/3,0

问题描述:

已知cos(a+π/4)=1/3,0

cos(a+π/4)=1/3
0sin(a+π/4)=2√2/3
cosa=cos(a+π/4-π/4)
=cos(a+π/4)cosπ/4+sin(a+π/4)sinπ/4
=1/3× √2/2+2√2/3× √2/2
=4+√2/6

cosa=[(√2)²+(√10)²-2²]/(2√2*√10)=2√5/5