Answer
$$\sqrt{\cos^2t}=\cos t$$
Pick $t=\pi$ and replace into $\cos t$ and $\sqrt{\cos^2t}$. The results came out differently, so the equation is not an identity.
Work Step by Step
$$\sqrt{\cos^2t}=\cos t$$
To prove this is not an identity, we need to find an example that counters the equation.
We can choose $t=\pi$.
At $t=\pi$, $$\cos t=\cos\pi=-1$$
while at the same time, $$\sqrt{\cos^2t}=\sqrt{\cos^2\pi}=\sqrt{(-1)^2}=\sqrt1=1$$
Since $-1\ne1$, that means $\cos t\ne\sqrt{\cos^2t}$ at $t=\pi$.
The equation, thus, cannot be an identity.
