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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