Question

Help please !!!!!!!!!!!
CSC B = 25/7 and the sec B =25/24 find tan B??

Answer 1

tanβ = 7/24

Explanation:

Given:

cscβ = 25/7

secβ = 25/24

tanβ = ?

Recall:

cscβ = 1/sinβ

secβ = 1/cosβ

tanβ = sinβ/cosβ

Rewrite and simplify:

tanβ = sinβ/cosβ

tanβ = (1/cscβ)/(1/secβ)

tanβ = (1/(25/7))/(1/(25/24))

tanβ = (7/25)/(24/25)

tanβ = (7/25)(25/24)

tanβ = (7*25)/(25*24)

tanβ = 175/600

tanβ = 35/120

tanβ = 7/24

Answer 2

tan β =
`(7)/(24)`

Explanation:

Using the identities

sin x =
`(1)/(cscx)` , cos x =
`(1)/(secx)` , tan x =
`(sinx)/(cosx)` , then

sinβ =
`(1)/((25)/(7) )` =
`(7)/(25)`

cos β =
`(1)/((25)/(24) )` =
`(24)/(25)`

Then

tan β =
`((7)/(25) )/((24)/(25) )` =
`(7)/(25)` ×
`(25)/(24)` =
`(7)/(24)`