Question

If 3 cot A = 4, where 0° < A < 90°, then sec A is equal to _________.

Options

• `5/4`

• `4/3`

• `5/3`

• `3/4`

Answer 1

If 3 cot A = 4, where 0° < A < 90°, then sec A is equal to `bbunderline(5/4)`.

Explanation:

3 cot A = 4

cot A = `4/3`

⇒ tan A = `1/cot A = 3/4`

As we know,

sec A = `sqrt(1 + ( tan A )^2`

= `sqrt(1 + ( 3/4 )^2`

= `sqrt (1 + 9/16)`

= `sqrt(16 + 9)/16`

= `sqrt25/16`

= `5/4`