Prove that cot4theta-1=cosec4theta-2cosec2theta

Question : Prove that cot⁴θ-1=cosec⁴θ-2cosec²θ

Doubt by Utkrisht

Solution : 

cot⁴θ-1=cosec⁴θ-2cosec²θ

RHS

=cosec⁴θ-2cpsec²θ
=cosec²θ(cosec²θ-2)

=(1+cot²θ)(1+cot²θ-2) [∵cosec²θ=1+cot²θ]
=1+cot²θ(cot²θ-1)
=(1+cot²θ)[-(1-cot²θ)]
=-(1+cot²θ)(1-cot²θ)
=-([1]²-[cot²θ]²) [∵(a+b)(a-b)=a²-b²]
=-(1-cot⁴θ)
=-1+cot⁴θ
=cot⁴θ-1

= LHS

LHS=RHS

Hence Proved.