Question

If sinx=(-15)/17 with π≤x≤3π/2 and cosy=3/5 with 0≤y≤π/2, find the exact value of cos⁡(x-y)

Answer 1

• sin(x)=(-15)/17
• cos(x)=(-8)/17
• cos(y)=3/5
• sin(y)=4/5

`→\cos(x - y) = \cos(x)\cos(y) + \sin(x) \sin(y) \\ =(( - 8)/(17)* (3)/(5)) +(( - 15)/(17) * (4)/(5)) \\ = ( - 24)/(85) + ( - 60)/(85) \\ = ( (- 24) + ( - 60))/(85) \\ = \boxed{ ( - 84)/(85) }✓`

(-84)/85 is the right answer.