Question

How do you solve `3cscx=2cscx+sqrt2` for `0<=x<=2pi`?

Answer 1

`pi/4; (3pi)/4`

Explanation:

Replace in the equation csc x by `1/(sin x)`:
`3/(sin x) - 2/(sin x) = sqrt2`
`1/(sin x) = sqrt2` -->
`sin x = 1/sqrt2 = sqrt2/2`
Trig table and unit circle -->
`x = pi/4 and x = (3pi)/4`
Answers for `(0, 2pi)`
`pi/4; (3pi)/4`