This should clear up. Its asking to prove y'. The equation given is:\[ y = \frac{x}{\sqrt{a^2 - 1}} - \frac{2}{\sqrt{a^2 - 1}} \arctan \left( \frac{\sin(x)}{a + \sqrt{a^2 - 1} \cdot (1 + \cos(x))} \right) \]1. **Expression Explanation**: - The equation is presented in a format involving trigonometric and inverse trigonometric functions. - The first term is a fraction, with the numerator \( x \) and the denominator \( \sqrt{a^2 - 1} \). - The second term involves the inverse tangent function \(\arctan\). - Inside the \(\arctan\), the fraction has \(\sin(x)\) as the numerator. - The denominator inside the \(\arctan\) is structured as \( a + \sqrt{a^2 - 1} \cdot (1 + \cos(x)) \).2. **Variables**: - \( y \) is expressed in terms of \( x \) and \( a \). - Both \( x \) and \( a \) influence the trigonometric components of the expression.This equation can be used in educational contexts to explain complex expressions involving trigonometric and inverse trigonometric functions as part of a precalculus or calculus curriculum. Transcription:"Show that \( y' = \frac{1}{a + \cos(x)} \)."

Answered: Image /qna-images/answer/86a3aa5d-ef59-46c2-a433-a37199d98ede.jpg

Answered: 2 sin(x) a + va? - 1 + cos(x) arctan…

2 sin(x) a + va? - 1 + cos(x) arctan Va? 1 Va? – 1 - - 1

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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