Question

4 sec x-csc x=O Solve?

Answer 1

See below.

Explanation:

`4secx-cscx=0`

`secx=1/cosx`

`cscx=1/sinx`

`4/cosx=1/sinx`

`(4cosx)/cosx=cosx/sinx`

`1/tanx=4`

`tanx=1/4`

`x=arctan(1/4)=0.24498 and 3.38657`

For:

`0<=x<=2pi`

Answer 2

`x = 14^@04 + k360^@`

Explanation:

`4/cos x = 1/sin x`
Multiply both sides by cos x (condition cos x != 0)
4 = cot x -->
`tan x = 1/4`
Calculator and unit circle give -->
`x = 14^@04 + k180^@`