Question

Simplify:

cos^2(a) /( sin(a)-1)

Answer 1

Answer:-1

Explanation:

`(cos^(2)a)/(sina-1) \\cos^(2)a=(1+cos2a)/(2)\\((1+cos2a)/(2))/(sina-1)=(1+cos2a)/(2(sina-1))=(1+cos2a)/(2sina-2)=(1+cos2a)/(-(2-2sina))\\1-2sina=cos2a\\(1+cos2a)/(-(1+(1-2sina)))=(1+cos2a)/(-(1+cos2a))=-1`

Answer 2

`\cfrac{cos^2(a)}{sin(a)-1}\implies \cfrac{1-sin^2(a)}{sin(a)-1}\implies \cfrac{\stackrel{ \textit{difference of squares} }{1^2-sin^2(a)}}{sin(a)-1} \\\\\\ \cfrac{[1-sin(a)][1+sin(a)]}{sin(a)-1}\implies \cfrac{~~\begin{matrix} [1-sin(a)] \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~[1+sin(a)]}{-[~~\begin{matrix} 1-sin(a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~]}\implies -[1+sin(a)]`