Answer
$sin~x = \sqrt{1-cos^2~x}~~~~$ is not an identity.
Work Step by Step
The graph of $sin~x$ includes both positive and negative values on the vertical axis. However, the graph of $\sqrt{1-cos^2~x}$ does not include any negative values on the vertical axis.
For example, $sin (\frac{3\pi}{2}) = -1$ but $\sqrt{1-cos^2~(\frac{3\pi}{2}}) = 1$
Therefore, $~~sin~x = \sqrt{1-cos^2~x}~~~~$ is not an identity.
