I am not sure how to find the $x$ values of $2\cos(2x)-2\sin(x)=0$.
I am trying to find the absolute values of $f(x)=2\cos(x)+\sin(2x)$ in the range$[0, \frac{\pi}{2}]$.
I have differentiated $f(x)$ to produce $2\cos(2x)-2\sin(x)$, but I am unsure how to find the zeros of the function since I cannot think of a value of $x$ that would make both sine and cosine equal 0.
$$\frac{d}{dx} 2\cos(x)=[0 \cdot \cos(x)] + [2 \cdot -\sin(x)]=-2\sin(x)$$ $$\frac{d}{dx}\sin(2x)= \cos(2x) (2)=2\cos(2x)$$
$$\frac{d}{dx}2\cos(x)+\sin(2x)=2\cos(2x)-2\sin(x)$$