Prove: $\frac{\cot \theta }{\mathrm{cosec}\theta -1}=\frac{\cos {\displaystyle \mathrm{ec}\theta }{\displaystyle +}{\displaystyle 1}}{\cot \theta }$.

Prove: $(\mathrm{secA}+\mathrm{cosA})(\mathrm{secA}-\mathrm{cosA})={\tan }^2\mathrm{A}+{\sin }^2\mathrm{A}$.

Prove: $1+3{cosec}^2\theta ·{\cot }^2\theta +{\cot }^6\theta ={cosec}^6\theta$.

Prove: $\frac{1-\mathrm{sec\theta }+\mathrm{tan\theta }}{1+\mathrm{sec\theta }-\mathrm{tan\theta }}=\frac{\mathrm{sec\theta }+\mathrm{tan\theta }-1}{\mathrm{sec\theta }+\mathrm{tan\theta }+1}$