130221
140221
140204
22023
Correct answer is B
cos(x+y)=cosxcosy−sinxsiny
Given sin of an angle implies we have the value of the opposite and hypotenuse of the right-angled triangle. We find the adjacent side using Pythagoras' theorem.
Adj2=Hyp2−Opp2
For triangle with angle x, adj=√132−52=√144=12
For triangle with angle y, adj=√172−82=√225=15
∴
\cos(x+y) = (\frac{12}{13}\times\frac{15}{17}) - (\frac{5}{13}\times\frac{8}{17}) = \frac{180}{221} - \frac{40}{221}
= \frac{140}{221}
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