Question

Please help, very confused!

Answer 1

$\bf cot(\theta)=\cfrac{1}{tan(\theta)} \qquad \qquad csc(\theta)=\cfrac{1}{sin(\theta)}\qquad \qquad sin(-\theta )=-sin(\theta ) \\\\\\ \textit{also recall }sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\ -------------------------------$

$\bf \cfrac{csc^2(x)-cot^2(x)}{sin(-x)cot(x)}\implies \cfrac{\frac{1}{sin^2(x)}-\frac{cos^2(x)}{sin^2(x)}}{-sin(x)\frac{cos(x)}{sin(x)}}\implies \cfrac{\frac{1-cos^2(x)}{sin^2(x)}}{-cos(x)} \\\\\\ \cfrac{\frac{sin^2(x)}{sin^2(x)}}{-cos(x)}\implies \cfrac{1}{-cos(x)}\implies -sec(x)$