Question

How do I solve this?

Answer 1

Answer: F

Explanation:

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

`\tan x=2 \implies \sin x=(2)/(√(5)), \cos x=(1)/(√(5))\\\\\sin y=(8)/(17) \implies \cos y=-(15)/(17)\\\\\sin (x+y)=\left((2)/(√(5)) \right) \left(-(15)/(17) \right)+\left((1)/(√(5)) \right) \left((8)/(17) \right)\\\\=-(30)/(17√(5))+(8)/(17√(5))\\\\=-(22)/(17√(5))\\\\=-(22√(5))/(85)`