Question

If tan A = `1/2`, then sin A is equal to ______.

Options

• `2/sqrt(5)`

• `1/sqrt(3)`

• `1/sqrt(5)`

• 1

Answer 1

If tan A = `1/2`, then sin A is equal to `underlinebb(1/sqrt(5))`.

Explanation:

Given, tan A = `1/2`

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

⇒ `sin A/sqrt(1 - sin^2A) = 1/2`   ...(∵ sin² A + cos² A = 1) 

⇒ 4 sin² A = 1 – sin² A

⇒ sin² A = `1/5`

⇒ sin A = `1/sqrt(5)`