sin(a+b)=0.86
sin(a-b)=0.34
What is sinbcosa?
(I did this question previously on the test by making two formulas, one for a and one for b and substituting the formulas into each other to figure out a and b separately, but now I don't remember how to do it (ps answer is 0.26)
+130466 sin (a + b) = sinacosb + sinbcosa = .86
sin (a - b) = sinacosb - sinbcosa = .34 add these
2sinacosb = 1.20 divide by 2
sinacosb = .60
Sub this into either of the first two equations
.60 + sinbcosa = .86 subtract .60 from each side
sinbcosa = .26
+26396 sin(a+b)=0.86
sin(a-b)=0.34
What is sinbcosa?
(1)sin(a+b)=sin(a)cos(b)+cos(a)sin(b)(2)sin(a−b)=sin(a)cos(b)−cos(a)sin(b)(1)−(2):sin(a+b)−sin(a−b)=sin(a)cos(b)+cos(a)sin(b)−[ sin(a)cos(b)−cos(a)sin(b) ]sin(a+b)−sin(a−b)=sin(a)cos(b)+cos(a)sin(b)−sin(a)cos(b)+cos(a)sin(b)sin(a+b)−sin(a−b)=sin(a)cos(b)−sin(a)cos(b)+cos(a)sin(b)+cos(a)sin(b)sin(a+b)−sin(a−b)=cos(a)sin(b)+cos(a)sin(b)sin(a+b)−sin(a−b)=2cos(a)sin(b)sin(a+b)−sin(a−b)=2sin(b)cos(a)sin(b)cos(a)=12⋅[sin(a+b)−sin(a−b)]|sin(a+b)=0.86sin(a−b)=0.34sin(b)cos(a)=12⋅(0.86−0.34)sin(b)cos(a)=12⋅(0.52)sin(b)cos(a)=0.26
