Question

How do you verify that the x values `pi/6, (5pi)/6` are solutions to `csc^4x-4csc^2x=0`?

Answer 1

By putting `x=pi/6` and `x=(5pi)/6` in `csc^4x-4csc^2x=0`

Explanation:

If `x=pi/6`, we have `cscx=2`

Therefore `csc^4x-4csc^2x=2^4-4xx2^2=16-16=0`

Similarly if `x=(5pi)/6` `cscx=2`

and again `csc^4x-4csc^2x=2^4-4xx2^2=16-16=0`

Hence `x=pi/6` and `x=(5pi)/6` are solutions to `csc^4x-4csc^2x=0`