## Calculus 8th Edition

$csc\phi$ $+cot\phi$ $=\frac{sin\phi}{1-cos \phi}$
Need to prove the identity $csc\phi$ $+cot\phi$ $=\frac{sin\phi}{1-cos \phi}$ Let us solve left side of the given identity. $csc\phi$ $+cot\phi$ $=\frac{1}{sin\phi}+\frac{cos \phi}{sin\phi}$ $=\frac{1+cos \phi}{sin\phi}$ $=\frac{1+cos \phi}{sin\phi}\times \frac{1-cos \phi}{1-cos\phi}$ $=\frac{1-cos^{2} \phi}{sin\phi(1-cos\phi)}$ $=\frac{sin^{2} \phi}{sin\phi(1-cos\phi)}$ Hence, $csc\phi$ $+cot\phi$ $=\frac{sin\phi}{1-cos \phi}$