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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