cos(θ + x) = \(\frac{3}{5}\), sin(θ + y) = \(\frac{5}{13}\). Find sin(x - y).
Answer & explanation
Correct answer: option 1
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) = \(\frac{4}{5}\) × \(\frac{12}{13}\) - \(\frac{3}{5}\) × \(\frac{5}{13}\) = \(\frac{33}{65}\)