Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 47: 79

Answer

Showed that given statement, $\tan\theta + \cot\theta$ = $\sec\theta\csc\theta$, is an identity as left side transforms into right side.

Work Step by Step

Given statement is- $\tan\theta + \cot\theta$ = $\sec\theta\csc\theta$ Left Side = $\tan\theta + \cot\theta$ = $\frac{\sin\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta}$ (Using ratio identity for $\tan\theta$ and $\cot\theta$) =$\frac{\sin\theta}{\sin\theta}.\frac{\sin\theta}{\cos\theta} +\frac{\cos\theta}{\sin\theta}. \frac{\cos\theta}{\cos\theta} $ =$\frac{\sin^{2}\theta}{\sin\theta\cos\theta} + \frac{\cos^{2}\theta}{\sin\theta\cos\theta} $ =$\frac{\sin^{2}\theta + \cos^{2}\theta}{\sin\theta\cos\theta}$ =$\frac{1}{\sin\theta\cos\theta}$ =$\frac{1}{\cos\theta}.\frac{1}{\sin\theta}$ = $\sec\theta\csc\theta$ = Right Side i.e. Left Side transforms into Right Side i.e. Given statement, $\tan\theta + \cot\theta$ = $\sec\theta\csc\theta$, is an identity.
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.