Question #c42b1

1 Answer
Jun 12, 2016

We will use the following:

  • cos(α+β)=cos(α)cos(β)sin(α)sin(β)
  • cos(αβ)=cos(α)cos(β)+sin(α)sin(β)
  • cos(45)=sin(45)=22

With those, we have

cos(θ+45)=cos(θ)cos(45)sin(θ)sin(45)

=22cos(θ)22sin(θ)

cos(θ45)=cos(θ)cos(45)+sin(θ)sin(45)

=22cos(θ)+22sin(θ)

Adding the two, we get

cos(θ+45)+cos(θ45)

=22cos(θ)22sin(θ)+22cos(θ)+22sin(θ)

=2(22cos(θ))

=2cos(θ)