sin(a-b)cosa-cos(b-a)sina=12/13,求cos(5π/4-b)
问题描述:
sin(a-b)cosa-cos(b-a)sina=12/13,求cos(5π/4-b)
和cos(π/3+2b)
答
sin(a-b)cosa-cos(a-b)sina=12/13
sin(a-b-a)=-sinb=12/13
sinb=-12/13
cos2b=1-2sin^2b=(169-288)/169=-119/169
cosb=±5/13
sin2b=2sinbcosb=120/169
cos(5π/4-b)
=cos5π/4cosb+sin5π/4sinb
=-√2/2cosb-√2/2sinb
.
cos(π/3+2b)=cosπ/3cos2b-sin(π/3)sin2b
,.