If A, B and C be the angles of a triangle, the incorrect relation is ?

Answer: Option C

$$\begin{array}{rl}& \text{A}+\text{B}+\text{C}=\pi =\text{18}{0}^{\circ }\\ & \Rightarrow \frac{\text{A + B}}{2}=\frac{{180}^{\circ }}{2}-\frac{\text{C}}{2}\\ & \Rightarrow \text{sin }\left(\frac{\text{A + B}}{2}\right)\\ & \Rightarrow \text{sin }\left(\frac{\pi }{2}-\frac{\text{C}}{2}\right)\\ & \Rightarrow \text{cos}\frac{\text{C}}{2}\\ & \\ & \mathbf{Similarly}:\\ & \text{cos }\left(\frac{\text{A}+\text{B}}{2}\right)=\text{sin}\frac{\text{C}}{2}\\ & \text{cot }\left(\frac{\text{A}+\text{B}}{2}\right)=\tan \frac{\text{C}}{2}\\ & \text{tan }\left(\frac{\text{A}+\text{B}}{2}\right)=\cot \frac{\text{C}}{2}\\ & \text{So, option C is incorrect}\text{.}\end{array}$$