Trigonometric identities

Answer: 1562510296​

1. Because θ is acute, cos(θ)=12544​.
2. sin(2θ)=2sin(θ)cos(θ).
3. Substitute the exact ratios to obtain sin(2θ)=1562510296​.

Answer: cos(7x)cos(3y)−sin(7x)sin(3y)

1. Apply the cosine compound-angle identity with u=7x and v=3y.
2. cos(7x+3y)=cos(7x)cos(3y)−sin(7x)sin(3y).

Answer: 5428932239​

1. Because θ is acute, cos(θ)=233208​.
2. cos(2θ)=cos2(θ)−sin2(θ).
3. Substitute the exact ratios to obtain cos(2θ)=5428932239​.