Not sure what these are called all I know is I need to prove em, but I dont know how.
Questions:
1. Prove: csc^2(θ)+cot^2(θ)-1
2. Prove: cot^2(w)/csc(w)-1=csc(w)+1
3. Prove: sec^4(α)-tan^4(α)=2sec^2(α)-1
$\displaystyle \displaystyle \begin{align*} \sec^4{a} - \tan^4{a} &\equiv \left(\sec^2{a} - \tan^2{a}\right)\left(\sec^2{a} + \tan^2{a}\right) \\ &\equiv 1\left(\sec^2{a} + \tan^2{a}\right) \\ &\equiv \sec^2{a} + \tan^2{a} \\ &\equiv \sec^2{a} + \sec^2{a} - 1 \\ &\equiv 2\sec^2{a} - 1 \end{align*} $