Question

If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.

Options

• 1

• 2

• 3

• 4

Answer 1

If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = 2.

Explanation:

Now, tan θ + cot θ = `sinθ/cosθ + cosθ/sinθ`

= `(sin^2θ + cos^2θ)/(cosθ sinθ)`

Putting sin²θ + cos²θ = 1

= `1/(cosθ sinθ)`  .....(1)

Finding cos θ sin θ

sin θ + cos θ = `sqrt(2)`

Squaring both sides

(sin θ + cos θ)² = `(sqrt(3))^2`

(sin θ + cos θ)² = 2

sin²θ + cos²θ + 2 sin θ cos θ = 2

Putting sin²θ + cos²θ = 1

1 + 2 sin θ cos θ = 2

2 sin θ cos θ = 2 – 1

2 sin θ cos θ = 1

sin θ cos θ = `1/2`

cos θ sin θ = `1/2`

Now, tan θ + cot θ = `1/(cos θ sin θ)`

Putting values

= `1/(1/2)`

= 2