Question

If sin θ + cos θ = √2, then tan θ + cot θ =​

Answer 1

2

Explanation:

sinθ + cosθ = √2

(sinθ + cosθ)² = (√2)²

sin²θ + cos²θ + 2sinθ cosθ = 2

1 + 2sinθ cosθ = 2

2sinθ cosθ = 1

sinθ cosθ =
`(1)/(2)`

tanθ + cotθ =
`(sin\theta)/(cos\theta) +(cos\theta)/(sin\theta)`

`=(sin^2\theta+cos^2\theta)/(sin\theta cos\theta)`

`=(1)/(sin\theta cos\theta)`

`=(1)/((1)/(2) )`

`=2`