Show that 3sin(theta) / (2 + cos(theta)) differs from theta by theta^5/180

Math Problem Statement

if thetha is small and positive show that 3sin thetha/ 2+cos thetha differs from thetha by about thetha ^5/180

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Trigonometry

Trigonometric identities

Small angle approximation

Undergraduate level

Understanding the Difference Between 3sin(theta)/(2+cos(theta)) and theta

Small Angle Approximation: Proving the Difference between 3sin(theta)/(2+cos(theta)) and Theta

Small-Angle Approximation: Simplifying Trigonometric Expressions

Simplified Small Angle Approximation of Trigonometric Expression

Limit of Trigonometric Functions: \(\lim_{\theta\to 0}\dfrac{1-\cos(\theta)}{2\sin^2(\theta)}\)