I've been working on this for a few hours... I have a mental block...
Verify the Identity:
[sin(2x)+sin(4x)] / [cos(2x) + cos(4x)] = tan(3x)
thanks so much, in advance
This should be easy if you can use Simpson's formulas (equations (1) and (3)) in the numerator and denominator...
(Happy)Hello, poolshark!
It's easy if we are allowed the Sum-to-Product identities:
. . $\displaystyle \begin{array}{ccc}\sin A + \sin B &=& 2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right) \\ \\ [-3mm]
\cos A + \cos B &=& 2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right) \end{array}$
The numerator is: .$\displaystyle \sin4x + \sin 2x \:=\:2\sin3x\cos x$Verify the identity: .$\displaystyle \frac{\sin2x+ \sin4x} {\cos2x + \cos4x} \:=\: \tan3x\$
The denominator is: .$\displaystyle \cos4x+\cos2x \:=\:2\cos3x \cos x$
The fraction becomes: .$\displaystyle \frac{{\color{blue}\rlap{/}}2\sin3x{\color{red}\rlap{/////}}\cos x}{{\color{blue}\rlap{/}}2\cos3x{\color{red}\rlap{/////}}\cos x} \;=\;\frac{\sin3x}{\cos3x} \;=\;\tan3x$