sin(pai/4-a)=5/13 0

问题描述:

sin(pai/4-a)=5/13 0

sin(π/4-a)=5/13,0<a<π/4a,得sin(a-π/4)=-5/13
得cos(a-π/4)=√(1-sin²(π/4-a)=12/13
sina=sin(a-π/4+π/4)=-5/13×√2/2+12/13×√2/2=7√2/26
cosa=cos(a-π/4+π/4)=12/13×√2/2-(-5/13)×√2/2=17√2/26
3sin²-4sinacosa+cos²a
=(sina-cosa)²+2sin²a-2sinacosa
=(sina-cosa)²+2sina(sina-cosa)
=50/169+2×7√2/26(-5√2/13)
=-20/169