find the range of the function : $y=(3\sin 2x-4\cos 2x)^2-5$ find the range of the function :
$$y=(3\sin 2x-4\cos 2x)^2-5$$
My try :
$$y=9\sin^22x+16\cos^22x-24\sin 2x\cos 2x-5\\y=9+7\cos^22x-12\sin4x-5$$
now what do I do؟

You can write $$3\sin 2x-4\cos 2x =5\sin(2x+\varphi)$$
for some constant angle $\varphi$, 
so $$ y = 25\sin^2(2x+\varphi)-5$$
so $y_{\max} = 20$ and $y_{\min} = -5$. 
