sin θ + cos θ = √2
Now square on both side
= ( sin θ + cos θ)2 = √22
= (sin2θ + cos2θ) + 2 sin θ cos θ = 2
= 1+ 2sin θ cos θ = 2
⇒ sin θ cos θ = \(\frac 12\)
Now
tanθ + cot θ = \(\frac{\sin \theta}{\cos\theta} + \frac{\cos\theta}{\sin \theta}\)
\(= \frac{\sin^2θ +\cos^2θ} { \sin θ \cos θ}\)
\(= \frac1{ \frac 12}\)
= 2
