Provide an Appropriate Response $\cot x = \frac { 1 } { x } - \left( \frac { x } { 3 } + \frac { x ^ { 3 } } { 45 } + \frac { 2 x ^ { 5 } } { 945 } + \ldots \right)$

question 354

Multiple Choice

Provide an appropriate response.
-Use the fact that $\cot x = \frac { 1 } { x } - \left( \frac { x } { 3 } + \frac { x ^ { 3 } } { 45 } + \frac { 2 x ^ { 5 } } { 945 } + \ldots \right)$ for $| x | < \pi$ to find the first four terms of the series for ln(sin $x$ ) .

• A) \(- \left( \frac { 1 } { x ^ { 2 } } + \frac { 1 } { 3 } + \frac { x ^ { 2 } } { 15 } + \frac { 2 x ^ { 4 } } { 189 } + \ldots \right)\)
• B) \(\frac { 1 } { x ^ { 2 } } + \frac { 1 } { 3 } + \frac { x ^ { 2 } } { 15 } + \frac { 2 x ^ { 4 } } { 189 } + \ldots\)
• C) \(\ln | x | - \left( \frac { x ^ { 2 } } { 6 } + \frac { x ^ { 4 } } { 180 } + \frac { x ^ { 6 } } { 2835 } + \ldots \right)\)
• D) \(- \ln | x | + \frac { x ^ { 2 } } { 6 } + \frac { x ^ { 4 } } { 180 } + \frac { x ^ { 6 } } { 2835 } + \ldots\)

---

Definitions:

Workout

A session of physical exercise designed to improve fitness, strength, or endurance.

Pleasant Activities

Activities that provide enjoyment, satisfaction, or relaxation, contributing to an individual's wellbeing.

Communication Skills

The ability to convey or exchange information effectively through verbal, non-verbal, written, and digital forms.

Health Care Professionals

Individuals licensed to provide medical services and advice to patients, ranging from doctors and nurses to therapists and pharmacists.