Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A32: 55


$csc\phi$ $+cot\phi$ $=\frac{sin\phi}{1-cos \phi}$

Work Step by Step

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, $csc\phi$ $+cot\phi$ $=\frac{sin\phi}{1-cos \phi}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.