Question

If sin A = `1/2`, then the value of cot A is ______.

Options

• `sqrt(3)`

• `1/sqrt(3)`

• `sqrt(3)/2`

• 1

Answer 1

If sin A = `1/2`, then the value of cot A is `underlinebb(sqrt(3))`.

Explanation:

According to the question,

sin A = `1/2`  ...(1)

We know that,

cot A = `1/(tan A) = (cos A)/(sin A)`  ...(2)

To find the value of cos A.

We have the equation,

sin² θ + cos² θ = 1

So, cos θ = `sqrt(1 - sin^2θ)`

Then,

cos A = `sqrt(1 - sin^2A)`  ...(3)

cos²A = 1 – sin²A

cos A = `sqrt(1 - sin^2A)`

Substituting equation 1 in 3, we get,

cos A = `sqrt(1 - 1/4)`

= `sqrt(3/4)`

= `sqrt(3)/2`

Substituting values of sin A and cos A in equation 2, we get

cot A = `(sqrt(3)/2) xx 2`

= `sqrt(3)`