已知cos(a+π/4)=3/5,π/2
问题描述:
已知cos(a+π/4)=3/5,π/2
答
因为cos(a+π/4)=3/5>0,a∈ [π/2,3π/2]
a+π/4∈ [3π/4,7π/4],
所以a∈ [5π/4,3π/2]
cos(2a+π/2)=2[cos(a+π/4)]^2-1=-7/25
a∈ [5π/4,3π/2]
2a+π/2∈ [3π,7π/2]
sin(2a+π/2)=-24/25
cos(2a+π/4)=cos(2a+π/2-π/4)
=cos(2a+π/2)cosπ/4+sin(2a+π/2)sinπ/4
=(-7/25-24/25)(根号2)2
=-31倍(根号2)/50