Question #a0e09

1 Answer
sente
Oct 10, 2016

Use that sine is an odd function, cosine is an even function, and the identity cos^2(theta)+sin^2(theta) = 1

Explanation:

We will use the following:

  • cos^2(theta)+sin^2(theta) = 1
  • cos(-theta) = cos(theta)
  • sin(-theta) = -sin(theta)

With those,

cos(theta)cos(-theta)-sin(theta)sin(-theta)

=cos(theta)(cos(theta))-sin(theta)(-sin(theta))

=cos(theta)cos(theta)+sin(theta)sin(theta)

=cos^2(theta)+sin^2(theta)

=1

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