Use an Addition or Subtraction Formula to find the exact value of the expression

Question

A.) cos(225º)

 

B.) tan (75º)

 

 

Answer 1

cos(180 + 45)

 

This angle is in the 3rd quadrant.  The reference angle is 45 degrees.  cos(45) is √(2)/2.  Since cosine is negative in the 3rd quadrant,

 

cos(225) = -√(2)/2

 

 

B)

 

cos(75) = cos(45 + 30)

 

            = cos(45)cos(30) - sin(45)sin(30)

 

            = (√(2)/2)(√(3)/2 - 1/2)

 

            = (√(6) /4) - (√(2) / 4)

 

            = (√(6) - √(2)) / 4