Ask Me Help Desk - Proving trigonometric identities

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proving trigonometric identities

(sin 3X + sin 7X) / (cos 7X + cos 3X) = tan 5X

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?

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