[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{cos^2(A)}{1+sin(A)}\implies \cfrac{1-sin^2(A)}{1-sin(A)}\implies \cfrac{\stackrel{\textit{difference of squares}}{1^2-sin^2(A)}}{1-sin(A)} \\\\\\ \cfrac{[1-sin(A)][1+sin(A)]}{1-sin(A)}\implies 1+sin(A)[/tex]
