I'm trying to solve the following question from my textbook.
Using the identity $\cos2\theta=2\cos^2\theta-1$ and $a\cos\theta+b\sin\theta=\sqrt{a^2+b^2}\cos(\theta-c)$, where $c$ is a constant, find the maximum and minimum values of $$11\cos^2\theta+3\sin\theta+6\sin\theta\cos\theta+5$$
$$\begin{align} 11\cos^2\theta+3\sin\theta+6\sin\theta\cos\theta+5 &=5.5(\cos2\theta+1)+3\sin\theta+3\sin2\theta+5 \\ &=5.5\cos2\theta+3\sin2\theta+3\sin\theta+10.5 \\ &=\sqrt{39.25}\cos(2\theta+28.610°)+3\sin\theta+10.5 \end{align}$$
And now I'm kind of stuck. Did I approach the question wrongly?