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

Solution (By Examveda Team)

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