Question

If `sqrt(2) sin θ = 1`, then cot θ × cosec θ is equal to ______.

Options

• `1/sqrt(2)`

• `1/(2sqrt(2))`

• `sqrt(2)`

• `1/2`

Answer 1

If `sqrt(2) sin θ = 1`, then cot θ × cosec θ is equal to `underlinebb(sqrt(2))`.

Explanation:

`sqrt(2) sin θ = 1`

`sin θ = 1/sqrt(2)`

⇒ sin θ = sin 45°   ...`(∵ sin 45^circ = 1/sqrt(2))`

⇒ θ = 45°

Now, cot θ × cosec θ

= cot 45° × cosec 45°   ...(∵ cot 45° = 1 and cosec `45^circ = sqrt(2)`)

= `1 xx sqrt(2)`

= `sqrt(2)`