Question

Sin(x-y) if cos x =8/17 and cos y = 3/5

Answer 1

`\sin(x-y)=\sin x\cos y-\sin y\cos x`

Since
`\cos x=\frac8{17}`, you have


`\sin x=√(1-\cos^2x)=\sqrt{1-\left(\frac8{17}\right)^2}=(15)/(17)`

and since
`\cos y=\frac35`, you have


`\sin y=√(1-\cos^2y)=√(1-\left(\frac35\right)^2)=\frac45`

So,


`\sin(x-y)=(15)/(17)*\frac35-\frac45*\frac8{17}=(13)/(85)`

Note that this assumes that both
`\sin x` and
`\sin y` are positive, or
`0<x<\pi`.