Final answer:
To find the exact value of each expression, use the trigonometric identities and angle sum formulas.
Step-by-step explanation:
To find the exact value of each expression, we can use the trigonometric identities and angle sum formulas.
(a) Using the formula for cos(A - B), we have:
cos(40° - 50°) = cos(40°)cos(50°) + sin(40°)sin(50°)
Plugging in the values, we get:
cos(40°)cos(50°) + sin(40°)sin(50°)
= (0.766)(0.643) + (0.643)(0.766)
= 0.493 + 0.493
= 0.986
(b) Applying the same formula, we have:
cos(37° - 7°) = cos(37°)cos(7°) + sin(37°)sin(7°)
Substituting the values, we get:
cos(37°)cos(7°) + sin(37°)sin(7°)
= (0.798)(0.991) + (0.602)(0.133)
= 0.791 + 0.080
= 0.871