F(x)=tan^-1(sin(cos^-1(x)))

Name: Problem 153, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-02-26T18:16:12-08:00
Duration: 59 s
Channel: Varsha Aggarwal
Description: f(x)=tan^-1(sin(cos^-1(x)))

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Key Concepts

Inverse Trigonometric Functions

This concept involves functions such as arctan and arccos, which return the angle whose trigonometric function equals the given value. Understanding their definitions, properties, and ranges is essential when dealing with compositions that invert standard trigonometric relationships.

Composition of Functions

When functions are composed, one function is applied to the result of another. In contexts involving trigonometric and inverse trigonometric functions, careful analysis of the output of one function as the input of another is needed, especially with regard to their respective domains and ranges.

Right Triangle Relationships

Using right triangle constructions can simplify complex trigonometric compositions by providing geometric interpretations. For instance, expressing a sine or cosine of an angle defined via an inverse trigonometric function often involves constructing a triangle to relate the sides and deducing the corresponding trigonometric value through the Pythagorean theorem.

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