Question

How do you solve `cosxcsc^2x+3cosx=7cosx`?

Answer 1

See below

Explanation:

`cosxcsc^2x+3cosx=7cosx`

`cosxcsc^2x-4cosx=0`

`cosx(csc^2x-4)=0`

`cosx=0`

`x=1/2npi, n = 2k+1, k in ZZ`

`csc^2x-4=0`

`csc^2x=4`

`cscx=+-2`

`sinx=+-1/2`

`x=(n +-1/3)pi, n =2k, k in ZZ`