If \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{15}{17}\), where A is an obtuse angle and B is acute, find the value of \(\cos (A + B)\).
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Correct Answer: Option n
Explanation:
\(\cos (A + B) = \cos A \cos B - \sin A \sin B\)
\(\sin A = \frac{3}{5} ; \cos B = \frac{15}{17}\)
\(\cos A = -\frac{4}{5}\) (A is obtuse)
\(\sin B = \frac{8}{17}\)
\(\cos (A + B) = \cos A \cos B - \sin A \sin B\)
= \((\frac{-4}{5} \times \frac{15}{17}) - (\frac{3}{5} \times \frac{8}{17})\)
= \(\frac{-60}{85} - \frac{24}{85}\)
= \(\frac{-84}{85}\)
\(\cos (A + B) = \cos A \cos B - \sin A \sin B\)
\(\sin A = \frac{3}{5} ; \cos B = \frac{15}{17}\)
\(\cos A = -\frac{4}{5}\) (A is obtuse)
\(\sin B = \frac{8}{17}\)
\(\cos (A + B) = \cos A \cos B - \sin A \sin B\)
= \((\frac{-4}{5} \times \frac{15}{17}) - (\frac{3}{5} \times \frac{8}{17})\)
= \(\frac{-60}{85} - \frac{24}{85}\)
= \(\frac{-84}{85}\)