cos(θ + x) = \(\frac{3}{5}\), sin(θ + y) = \(\frac{5}{13}\). Find sin(x - y).

\(\frac{33}{65}\) \(\frac{40}{27}\) \(\frac{34}{67}\) 1

\(\frac{33}{65}\)

Using sin(x-y) = sin{(θ+x) - (θ+y)} = sin(θ+x) cos(θ+y) - cos(θ+x) sin(θ+y) ⇒ Here, cos(θ+x) = \(\frac{3}{5}\), sin(θ+y) = \(\frac{5}{13}\) Put these values, ⇒ sin(x-y) = \(\frac{4}{5}\) × \(\frac{12}{13}\) - \(\frac{3}{5}\) × \(\frac{5}{13}\) = \(\frac{33}{65}\)