Question

Given cot θ = 3, the value of cos θ is ______.

विकल्प

• `1/3`

• `1/sqrt(10)`

• `3/sqrt(10)`

• `sqrt(10)/3`

Answer 1

Given cot θ = 3, the value of cos θ is `underlinebb(3/sqrt(10))`.

Explanation:

1. Identify the sides

The cotangent ratio is defined as:

`cot θ = "Adjacent"/"Opposite"`

= `3/1`

So, we can let:

Adjacent side (a) = 3

Opposite side (o) = 1

2. Find the Hypotenuse

Using the Pythagorean theorem (h² = a² + o²):

h² = 3² + 1²

h² = 9 + 1 = 10

`h = sqrt(10)`

3. Calculate cos θ

The cosine ratio is defined as:

`cos θ = "Adjacent"/"Hypotenuse"`

`cos θ = 3/sqrt(10)`