given that sin(a+b)= 56/65, cos(a+b)-33/65, cos(b)=-12/13 and pi/2<b<pi
Find:
sin(a)?
cos(a)?
tan(a)?
Assuming that cos(a+b) = -33/65
sin(a+b) = sin a cos b + cos a sin b
cos(a+b) = cos a cos b - sin a sin b
-12/13 sin a + 5/13 cos a = 56/65
5/13 sin a + 12/13 cos a = -33/65
Multiply by 5 to clear denominators:
-60 sin a + 25 cos a = 56
25 sin a + 60 cos a = -33
sin a = -507/845
cos a = 676/845
so,
tan a = -507/676