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؟

Hints:

Every real number $t$ can be expressed as $2x$ for some $x$, so the range of the function
$$f(x) = (3\sin 2x-4\cos 2x)^2-5$$
is the same as the range of
$$g(t)=(3\sin t-4\cos t)^2-5$$

But the expression
$$3\sin t-4\cos t$$
can be expressed as
$$5\left({\small{\frac{3}{5}}}\sin t-{\small{\frac{4}{5}\cos t}}\right)$$
which suggests what formula?
