cos (x+y)=cos x.cos y -sin x.sin y
Data:
sin x=12/13
cos x=5/13
sin y=8/17
cos y=15/17
therefore:
cos (x+y)=cos x.cos y -sin x.sin y
cos (x+y)=(5/13)(15/17)-(12/13)(8/17)
cos (x+y)=75/221-96/221
cos (x+y)=-21/221
Answer: cos (x+y)=-21/221
We can check it out our answer:
sin x=12/13
x=sin⁻¹(12/13)≈67.38
y=sin (8/17)≈28.07
(x+y)=67.38 + 28.07=95.45
(x+y)=cos⁻¹(-21/221)=95.45
