If sinθ + cosθ = $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is?

Solution (By Examveda Team)

$$\eqalign{ & \sin \theta + \cos \theta = \sqrt 2 \sin \left( {{{90}^ \circ } - \theta } \right) \cr & \sin \theta + \cos \theta = \sqrt 2 cos\theta \cr & {\text{Divide both sides by cos}}\theta \cr & {\text{tan}}\theta + 1 = \sqrt 2 \cr & \cot \theta = \frac{1}{{\sqrt 2 - 1}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 2 + 1 \cr} $$