1 - cot^4x = 2csc²x - csc^4x

the ^4 means to the fourth power. The x's are not supposed to be raised.

On the left side of the parentheses, rewrite:

1-(cot^{2}(x))^{2}

=1-(csc^{2}(x)-1)^{2}

Now, expand and you will see it.