Question

Given that sin(a) = 2 5 and cos(b) = − 1 3 , with a and b both in the interval 2 , , find the exact values of sin(a + b) and cos(a − b). sin(a + b) = cos(a − b) =

Answer 1

To find sin(a + b) and cos(a - b), use the trigonometric identities sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a - b) = cos(a)cos(b) + sin(a)sin(b). Substitute the given values and solve.

Step-by-step explanation:

To find the exact values of sin(a + b) and cos(a - b), we can use the trigonometric identities and the given values of sin(a) and cos(b). First, we can find sin(a + b) using the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Substituting the given values, we have sin(a + b) = (2/5)(-1/3) + cos(a)sin(b).

Next, to find cos(a - b), we can use the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b). Substituting the given values, we have cos(a - b) = (2/5)(-1/3) + cos(a)sin(b).