Question

I NEED HELP PLEASEE

Answer 1

`\bf \cfrac{1+cot^2(\theta )}{1+csc(\theta )}=\cfrac{1}{sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\implies \cfrac{1+(cos^2(\theta ))/(sin^2(\theta ))}{1+(1)/(sin(\theta ))}\implies \cfrac{~~(sin^2(\theta )+cos^2(\theta ))/(sin^2(\theta ))~~}{(sin(\theta )+1)/(sin(\theta ))}\implies \cfrac{~~(1)/(sin^2(\theta ))~~}{(sin(\theta )+1)/(sin(\theta ))}`

`\bf \cfrac{1}{\underset{sin(\theta )}{~~\begin{matrix} sin^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}\cdot \cfrac{~~\begin{matrix} sin(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{sin(\theta )+1}\implies \cfrac{1}{sin^2(\theta )+sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\\e \cfrac{1}{sin(\theta )}~\hfill`