Trigonometry 7th Edition

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

Chapter 5 - Section 5.1 - Proving Identities - 5.1 Problem Set - Page 280: 82

Answer

The equation is not an identity. A counterexample: $\theta=0.$

Work Step by Step

Graphing utility used: online calculator, desmos.com. (see below) The graphs of the two expressions are not equal, implying that the equation is not an identity. A counterexample is $\theta=0$, for which LHS=undefined (cot0 is undefined) RHS=$\displaystyle \frac{0+1}{1}=1$ LHS$\neq$RHS, so the equation is not an identity
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