Question #f676d

1 Answer
sente
Oct 19, 2016

We will use the double angle identities

  • sin(2theta) = 2sin(theta)cos(theta)

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

Proceeding...

1/2sin(4x) = 1/2sin(2(2x))

= 1/2(2sin(2x)cos(2x))

=sin(2x)cos(2x)

=(2sin(x)cos(x))(1-2sin^2(x))

=2sin(x)cos(x)(1) - (2sin(x)cos(x))(2sin^2(x))

=2sin(x)cos(x) - 4sin^3(x)cos(x)

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