Addition or Subtraction Formula

Question

Use an addition or subtraction formula to complete the following two steps: write the expression as a trigonometric function of one number, and then find its exact value. Do not use a calculator

cos (5pi/18) cos (pi/9) + sin (5pi/18) sin (pi/9)

Answer 1

We can use the formula cos(x)cos(y) + sin(x)sin(y) = cos(x - y) to solve the formula. In other words:

cos(5pi/18)cos(pi/9) + sin(5pi/18)sin(pi/9) = cos(5pi/18 - pi/9)

We can simplify with common denominators:

cos(5pi/18 - 2pi/18) = cos(3pi/18) = cos(pi/6) = √3/2