1. ## Trig identity question!

Another question I have unfortunately drawn a blank on..
Any help is greatly appreciated!

2. $\displaystyle \sin x(\cos y+2\sin y)=\cos x(2\cos y-\sin y)\Leftrightarrow$

$\displaystyle \Leftrightarrow\sin x\cos y+2\sin x\sin y=2\cos x\cos y-\sin y\cos x\Leftrightarrow$

$\displaystyle \Leftrightarrow \sin x\cos y+\sin y\cos x=2(\cos x\cos y-\sin x\sin y)\Leftrightarrow$

$\displaystyle \Leftrightarrow\sin(x+y)=2\cos(x+y)\Leftrightarrow \tan(x+y)=2$

3. ## Re :

$\displaystyle \sinx\cosy+2 \sinx\siny=2 \cosx\siny-\cosx\siny$

$\displaystyle \sinx\cosy+\cosx\siny=2(\cosx\cosy-\sinx\siny)$

$\displaystyle \sin(x+y)=2cos(x+y)$

$\displaystyle \frac{\sin(x+y)}{cos(x+y)}=2$

$\displaystyle \tan(x+y)=2$

Sorry about some confusion .. Can someone pls check my latex .

4. Ah I see now, I tried expanding it, but I see now you can swap them around so they fit into the sin and cos addition formulae.
Problem with these questions as its often very hard if you don't see the method you need to use at the beginning.

Cheers!