\(csc^4x-2csc^2x+1=cot^4x\)
csc^4x-2csc^2x+1=cot^4x
LHS=
\(LHS=cosec^4x-2cosec^2x+1\\ LHS=(cosec^2x-1)^2\\ LHS=\left(\frac{1-sin^2x}{sin^2x}\right)^2\\ LHS=\left(\frac{cos^2x}{sin^2x}\right)^2\\ LHS=\left(cot^2x\right)^2\\ LHS=cot^4x\\~\\ LHS=RHS \qquad QED\)