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View Full Version : Proving trigonometric identities


momoy001
Mar 12, 2010, 08:48 PM
(sin 3X + sin 7X) / (cos 7X + cos 3X) = tan 5X

galactus
Mar 14, 2010, 06:35 AM
Use the sum-to-product formulas and it is quite easy.

sin(u)+sin(v)=2sin(\frac{u+v}{2})cos(\frac{u-v}{2})

cos(u)+cos(v)=2cos(\frac{u+v}{2})cos(\frac{u-v}{2})

sin(3x)+sin(7x)=2sin(5x)cos(2x)

cos(7x)+cos(3x)=2cos(5x)cos(2x)

\frac{2sin(5x)cos(2x)}{2cos(5x)cos(2x)}

Now, see it?