Answer
The appropriate sign in order to make the computation true is the negative (–) sign.
Work Step by Step
We have the $\cos \,{{100}^{\circ }}$ that lies in the second quadrant where the trigonometric functions of sine and cosec are considered to be positive and the rest of the functions like cos, tan, sec, and cot are negative. The main reason that it lies in the second quadrant is that the first quadrant is $0\text{ to }{{90}^{\circ }}$ and the second quadrant is between ${{90}^{\circ }}\,\text{ and }\,{{180}^{\circ }}$.
Thus, this indicates that $\cos \,{{100}^{\circ }}$ is in the second quadrant where the sin and cosec are positive and the rest are negative.
