Question

If 2 tan A = 3, then value of sec A equals

Options

• `sqrt(13/2)`

• `sqrt(13)/4`

• `2/sqrt(13)`

• `sqrt(13)/2`

Answer 1

`bb(sqrt(13)/2)`

Explanation:

Given:

2 tan A = 3

`tan A = 3/2`

Using the identity:

sec² A = 1 + tan² A

`sec^2 A = 1 + (3/2)^2`

`sec^2 A = 1 + 9/4`

`sec^2 A = (4 + 9)/4`

`sec^2 A = 13/4`

`sec A = sqrt(13)/sqrt(4)`

`sec A = sqrt(13)/2`