Question #2f091

1 Answer
sente
Aug 23, 2016

We will use the following:

  • tan(theta) = sin(theta)/cos(theta)
  • sec(theta) = 1/cos(theta)
  • tan^2(theta)+1 = sec^2(theta)
  • sin(2theta) = 2sin(theta)cos(theta)

With those:

(12tan(a))/(1+tan^2(a)) = 6(2tan(a))/(1+tan^2(a))

=6(2tan(a))/sec^2(a)

=6(2tan(a)*cos^2(a))/(sec^2(a)*cos^2(a)

=6(2sin(a)/cos(a)*cos^2(a))/(1/cos^2(a)*cos^2(a))

=6(2sin(a)cos(a))

=6sin(2a)

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