Question

已知sina=-3/5,a是第四象限角，求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值

Answer 1

解：a是第四象限角，cosa=4/5,tana=-3/4
sin(π/4-a)=sinπ/4cosa-cosπ/4sina=7√2/10
cos(π/4+a)=cosπ/4cosa-sinπ/4sina=7√2/10
tan(a-π/4)=(tana-tanπ/4)/(1+tanatanπ/4)=-7
希望采纳，谢谢！

Answer 2

解:cosa=4/5
原式=sin45度cosa-cos45度sina
=根号下2/2*4/5+根号下2/2*3/5
=8/5*根号下2/2

Answer 3

sina=-3/5,且a是第四象限角，所以cosa=4/5,tana=-3/4,(sinπ/4=√2/2,cosπ/4=√2/2,tanπ/4=1)
sin(π/4-a)
=sinπ/4·cosa-cosπ/4·sina
=√2/2·4/5-√2/2·(-3/5)
=√2/10
同理，可算出cos(π/4+a)=（7√2）/10
tan(a-π/4)
=(tana-tanπ/4)/(1+tanatanπ/4)
=(-3/4-1)·(1+-3/4*1)
=-7/16
过程就是这样，不知道是否有算错的地方，你自己在检验一下