Question

If sinθ + cosθ = √2, then tanθ + cot θ = 

(a) 1 

(b) 2 

(c) 3 

(d) 4

Answer 1

(b) 2

Sinθ + cosθ = √2 ⇒ (sinθ + cosθ)² = 2 

⇒ sin²θ + cos²θ + 2 sinθ cosθ = 2

⇒ 1 + 2 sinθ cosθ = 2 

⇒ Sinθ cosθ = 2-1/2 = 1/2

tanθ + cotθ = sinθ/cosθ + cosθ/sinθ

= \(\frac{sin^2\theta + cos^2 \theta}{sin\theta cos\theta}\)

= \(\frac{1}{sin\theta\, cos\theta}\)

= \(\frac{1}{\frac{1}{2}}\) = 2