Question

If `sin θ = sqrt(3)/2` then (cosec θ + cot θ) = ?

Options

• `(2 + sqrt(3))`

• `2sqrt(3)`

• `sqrt(2)`

• `sqrt(3)`

Answer 1

`bb(sqrt(3))`

Explanation:

cos² θ = (1 – sin² θ) 

= `(1 - 3/4)`

= `1/4`

⇒ `cos θ = 1/2`

∴ `"cosec"  θ = 1/(sin θ) = 2/sqrt(3)` and `cot θ = (cos θ)/(sin θ) = ((1/2))/((sqrt(3)/2)) = 1/sqrt(3)`

∴ `("cosec"  θ + cot θ) = (2/sqrt(3) + 1/sqrt(3))`

= `3/sqrt(3)`

= `sqrt(3)`