How do you verify the identity: -cotx =(sin3x+sinx)/(cos3x-cosx)?

1 Answer
Massimiliano
Feb 6, 2015

There are some formulas, named sum-to-product, that say:

sintheta+sinphi=2sin((theta+phi)/2)cos((theta-phi)/2),
sintheta-sinphi=2cos((theta+phi)/2)sin((theta-phi)/2),
costheta+sinphi=2cos((theta+phi)/2)cos((theta-phi)/2),
costheta+cosphi=-2sin((theta+phi)/2)sin((theta-phi)/2).

So:

-cotx=(2sin((3x+x)/2)cos((3x-x)/2))/(-2sin((3x+x)/2)sin((3x-x)/2));

-cotx=-(cosx)/sinx.

That's all.

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