已知cos(a+π/4)=3/5,a∈ [π/2,3π/2],求cos(2a+π/4)

问题描述:

已知cos(a+π/4)=3/5,a∈ [π/2,3π/2],求cos(2a+π/4)

因为cos(a+π/4)=3/5>0,a∈ [π/2,3π/2]a+π/4∈ [3π/2,7π/4],所以a∈ [5π/4,3π/2]cos(2a+π/2)=2[cos(a+π/4)]^2-1=-7/25a∈ [5π/4,3π/2]2a+π/2∈ [3π,7π/2]sin(2a+π/2)=-24/25cos(2a+π/4)=c...