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)).
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})