What Trig Identities can you use to solve this problem?

#tan(x)*sin(x)*cos(x)+cos(2x)#

1 Answer
Jigy
May 29, 2018

#tan(x)*sin(x)*cos(x)+cos(2x) = cos^2(x)#

Explanation:

Identities used:

  1. #tan(x)=sin(x)/cos(x)#
  2. #cos(2x) = cos^2(x) - sin^2(x)#

#tan(x)*sin(x)*cos(x)+cos(2x)#
#=sin(x)/cancel(cos(x))*sin(x)*cancel(cos(x))+cos(2x)#
#=sin^2(x)+cos(2x)#
#=sin^2(x)+cos^2(x) - sin^2(x)#
#=cancel(sin^2(x))+cos^2(x) - cancel(sin^2(x))#
#= cos^2(x)#

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