Sin65.cos5-sin5.cos65
To solve the expression Sin65.cos5-sin5.cos65, we need to use trigonometric identities and the values of sine and cosine for specific angles.
First, we can simplify the expression using the difference-of-angles identity for sine:
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
In this case, A = 65 and B = 5, so we have:
sin(65 - 5) = sin(65)cos(5) - cos(65)sin(5)
Now, we need to determine the values of sin(65) and cos(65).
Using a calculator or trigonometric tables, we find that sin(65) ≈ 0.9063 and cos(65) ≈ 0.4226.
Similarly, we find that sin(5) ≈ 0.0872 and cos(5) ≈ 0.9962.
Now, we can substitute these values into the expression:
sin(65)cos(5) - cos(65)sin(5) ≈ (0.9063)(0.9962) - (0.4226)(0.0872)
≈ 0.9030 - 0.0369
≈ 0.8661
So, the value of Sin65.cos5-sin5.cos65 is approximately 0.8661.