Answer
$$\sec(\pi-x)=-\sec x$$
We attempt the left side first to reach the conclusion that the equation is an identity.
Work Step by Step
$$\sec(\pi-x)=-\sec x$$
We attempt from the left side first.
$$A=\sec(\pi-x)$$
It is known that $$\sec\theta=\frac{1}{\cos\theta}$$
which means
$$A=\frac{1}{\cos(\pi-x)}$$
Now we expand $\cos(\pi -x)$ according to the cosine difference identity, which states
$$\cos(A-B)=\cos A\cos B+\sin A\sin B$$
$$A=\frac{1}{\cos\pi\cos x+\sin\pi\sin x}$$
$$A=\frac{1}{-1\times\cos x+0\times\sin x}$$
$$A=\frac{1}{-\cos x}$$
$$A=-\frac{1}{\cos x}$$
$$A=-\sec x$$ (as $\sec\theta=\frac{1}{\cos\theta}$)
The equation is true, so it is an identity.
