If tanθ - cotθ = 0 find the value of sinθ + cosθ ?

Answer: Option C

$$\begin{array}{rl}& \text{tan}\theta -\cot \theta =0\\ & \mathbf{Shortcut}\mathbf{method}:\\ & \text{Put }\theta =45^{\circ }\\ & \text{tan }45^{\circ }-\cot 45^{\circ }=0\\ & 1-1=0\\ & 0-0(\text{matched})\\ & So,\theta =45^{\circ }\\ & \Rightarrow \sin \theta +\cos \theta \\ & \Rightarrow \sin 45^{\circ }+\cos 45^{\circ }\\ & \Rightarrow \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\\ & \Rightarrow \sqrt{2}\end{array}$$