Double- and Half-Angle Formulas

Here they are:

sin2(theta)=2sin(theta)cos(theta)

cos2(theta)=cos^2(theta)-sin^2(theta)

cos2(theta)=1-2sin^2(theta)

cos2(theta)=2cos^2(theta)-1

tan2(theta)=2tan(theta)/1-tan^2(theta)

sin theta/2=+/-square root of 1-cos(theta)/2

cos theta/2=+/-square root of 1+cos(theta)/2

tan theta/2=+/-square root of 1-cos(theta)/1+cos(theta)

tan theta/2=sin(theta)/1+cos(theta)

tan theta/2=1-cos(theta)/sin(theta)

Example:

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Simplify.

cos^2(pi/12) - sin^2(pi/12)

=cos2(pi/12)

=cos2(15)

=cos30 degrees

=sqrt of 3/2