Find the exact value of the trig function below.

cos(x+y) if sinx = [tex] \frac{12}{13} [/tex], cosx = [tex] \frac{5}{13} [/tex], siny = [tex] \frac{8}{17} [/tex], and cosy = [tex] \frac{15}{17} [/tex]

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

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Find the exact value of the trig function below. cos(x+y) if sinx = [tex] \frac{12}{13} [/tex], cosx = [tex] \frac{5}{13} [/tex], siny = [tex] \frac{8}{17} [/tex], and cosy = [tex] \frac{15}{17} [/tex]

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Find the exact value of the trig function below.

cos(x+y) if sinx = [tex] \frac{12}{13} [/tex], cosx = [tex] \frac{5}{13} [/tex], siny = [tex] \frac{8}{17} [/tex], and cosy = [tex] \frac{15}{17} [/tex]