已知sina=15/17,cosb=-5/13,求sin(a+b),cos(a-b),(tana+b)已知sina=15/17,cosb=-5/13,且a,b都是第二象限角.求sin(a+b),cos(a-b),(tana+b)的值而且一楼你的答案错了 ,sin b和cos a是怎么算出来的?

Question

已知sina=15/17,cosb=-5/13,求sin(a+b),cos(a-b),(tana+b)
已知sina=15/17,cosb=-5/13,且a,b都是第二象限角.求sin(a+b),cos(a-b),(tana+b)的值
而且一楼你的答案错了
,sin b和cos a是怎么算出来的?

Answer 1

cosa=-8/17
sinb=12/13
tga=-15/8
tgb=-12/5
sin(a+b)
=sinacosb+cosasinb
=15/17*(-5/13)+(-8/17)*12/13
=（-75-96)/221
=-171/221
cos(a-b)
=cosacosb+sinasinb
=(-8/17)*(-5/13)+15/17*12/13
=40/221+180/221
=220/221
tg(a+b)
=(tga+tgb)/(1-tgatgb)
=(-15/8-12/5)/[1-(-15/8)*(-12/5)]
=(-15/8-12/5)/[1-9/2]
=(-171/40)/(-7/2)
=171/40*2/7
=171/140