Question

Csc^3x-csc^2x-cscx+1=cot^2x(cscx-1)​

Answer 1

Sorry, I messed up. So I changed it.

Answer 2

Verify the identity:

`csc^3x-csc^2x-cscx+1\qquad =cot^2x(cscx-1)\\\\csc^2x(cscx-1)-1(cscx-1) =\quad \downarrow\\\\(csc^2x-1)(cscx-1)\quad \qquad \ =\quad \downarrow\\\\\bigg((1)/(sin^2x)-(sin^2x)/(sin^2x)\bigg)(cscx-1)\ =\quad \downarrow\\\\\\\bigg((1-sin^2x)/(sin^2x)\bigg)(cscx-1)\qquad \ =\quad \downarrow\\\\\\\bigg((cos^2x)/(sin^2x)\bigg)(cscx-1)\qquad \qquad =\quad \downarrow\\\\\\cot^2x(cscx-1)\qquad \qquad \qquad =cot^2x(cscx-1)\qquad \checkmark`