Question

If sin A = `3/5`, then value of cot A is ______.

विकल्प

• `3/4`

• `4/3`

• `4/5`

• `5/4`

Answer 1

If sin A = `3/5`, then value of cot A is `\underlinebb(4/3)`.

Explanation:

We have sin A = `3/5`

As sin A = `"p"/"h"`

Let perpendicular = 3x and hypotenuse = 5x.

Also, let ABC be a right angled Δ.

5x	3x
A	B

AC = `sqrt("AB"^2 + "BC"^2)` (By using Pythagoras theorem)

`5x = sqrt("AB"^2 + (3x)^2)`

(5x)² = AB² + 9x²

AB² = 25x² − 9x²

AB² = 16x²

⇒ AB = 4x

Thus, Base = 4x

Hence, cot A = `"B"/"P" = (4x)/(3x) = 4/3`