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

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Answer 1 · 2017-02-19T07:02:10

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

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 $csc^4x-4csc^2x=0$

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