Question

If cos A = `4/5`, then the value of tan A is ______.

Options

• `3/5`

• `3/4`

• `4/3`

• `5/3`

• `1/8`

Answer 1

If cos A = `4/5`, then the value of tan A is `underlinebb(3/4)`.

Explanation:

According to the question,

cos A = `4/5`     ...(1)

We know,

tan A = `(sin A)/(cos A)`

To find the value of sin A,

We have the equation,

sin²θ + cos²θ = 1

So, sin θ = `sqrt(1 - cos^2θ)`

Then,

sin A = `sqrt(1 - cos^2A)`    ...(2)

sin²A = 1 – cos²A

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

Substituting equation (1) in (2),

We get,

sin A = `sqrt(1 - (4/5)^2)`

= `sqrt(1 - (16/25))`

= `sqrt(9/25)`

= `3/4`

Therefore, tan A = `3/5 xx 5/4 = 3/4`.