Need help with the sum/difference formula?

Question

Im having trouble using the sum/difference formula to simplify the equations below. Help is greatly appreciated

 

 

1) cos (π + θ)

2) tan (π/6 + π)

3) sin (π/4 - π/2)

 

π = "pi"

Answer 1

(1). cos(π+θ) = cosπcosθ - sinπsinθ

                       = (-1)cosθ - (0)sinθ = -cosθ

 

(3). sin(π/4 - π/2)

                  = sin(π/4)cos(π/2) - cos(π/4)sin(π/2)

                  = (√2/2)(0) - (√2/2)(1)

                  = -√2/2

 

(2).  tan(π/6 + π)

            = {tan(π/6) + tan(π)}/{1-tan(π/6)tan(π)}

            = {√3/3 + 0}/{1 - 0}

            = √3/3