Question

In a right triangle ABC, right-angled at A, if sin B = `1/4`, then the value of sec B is ______.

पर्याय

• 4

• `sqrt15/4`

• `sqrt15`

• `4/sqrt15`

Answer 1

In a right triangle ABC, right-angled at A, if sin B = `1/4`, then the value of sec B is `bbunderline(4/sqrt15)`.

Explanation:

sin B = `1/4`

Sin² B + cos² B = 1

`(1/4)^2 + cos^2 B = 1`

`1/16 + cos^2 = 1`

cos² B = `1 - 1/16`

cos² B = `(16 - 1)/16`

cos² B = `15/16`

cos B = `sqrt((15)/(4 xx 4))`

cos B = `sqrt15/4`

∴ sec B = `1/cos B`

= `1/(sqrt15/4)`

= `4/sqrt15`