Question

So I have to establish an identity...

csc^4Ѳ-csc^2Ѳ=cot^4Ѳ+cot^2Ѳ can someone help me work through this please? I'd greatly appreciate it.

Answer 1

Left side:
\[\csc^4θ-csc^2θ\]
\[=\csc^2θ(\csc^2θ-1)\]
\[=\csc^2θ \cot^2θ\]

Right side:
\[\cot^4θ+\cot^2θ\]
\[=\cot^2θ(\cot^2θ+1)\]
\[=\cot^2θ\csc^2θ\]

∵ LS = RS
∴ QED

Answer 2

Thank you bunches!