Question

For #103 I need to know how to prove it's an identity

Answer 1

`\bf cot(x)+sin(x)=\cfrac{1+cos(x)-cos^2(x)}{sin(x)}\\\\ -----------------------------\\\\ \textit{now, recall your pythagorean identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\ -----------------------------\\\\ thus\qquad \cfrac{1+cos(x)-cos^2(x)}{sin(x)}\implies \cfrac{\boxed{1-cos^2(x)}+cos(x)}{sin(x)} \\\\\\ \cfrac{\boxed{sin^2(x)}+cos(x)}{sin(x)}\implies \cfrac{sin^2(x)}{sin(x)}+\cfrac{cos(x)}{sin(x)}\implies\cfrac{cos(x)}{sin(x)}+ \cfrac{sin^2(x)}{sin(x)} \\\\`


`\bf cot(x)+sin(x)`