Question

For an acute angle θ, if `sin θ = 1/9`, then value of `(9  "cosec"  θ + 1)/(9  "cosec"  θ - 1)` is ______.

Options

• 0

• `80/81`

• 1

• `82/80`

Answer 1

For an acute angle θ, if `sin θ = 1/9`, then value of `(9  "cosec"  θ + 1)/(9  "cosec"  θ - 1)` is `underlinebb(82/80)`.

Explanation:

Given: `sin θ = 1/9`

Therefore, `"cosec"  θ = 1/(sin θ) = 9`.

`(9  "cosec"  θ + 1)/(9  "cosec"  θ - 1)`

= `(9(9) + 1)/(9(9) - 1)`

= `(81 + 1)/(81 - 1)`

= `82/80`