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5. Simplify the expression: tan (csc (x)). Assume x is defined appropriately.

5. Simplify the expression: tan (csc (x)). Assume x is defined appropriately.

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Problem 36:** Simplify the expression: \( \tan \left( \csc^{-1}(x) \right) \). Assume \( x \) is defined appropriately. In this problem, we are asked to simplify the expression involving trigonometric functions, specifically the tangent of the inverse cosecant of \( x \). Notice that \( \csc^{-1}(x) \) is the inverse cosecant function, which implies that we are considering the angle whose cosecant value is \( x \). We assume that \( x \) is appropriately defined, meaning that it satisfies the domain restrictions for the inverse cosecant function, \( x \geq 1 \) or \( x \leq -1 \), excluding 0.
Transcribed Image Text:**Problem 36:** Simplify the expression: \( \tan \left( \csc^{-1}(x) \right) \). Assume \( x \) is defined appropriately. In this problem, we are asked to simplify the expression involving trigonometric functions, specifically the tangent of the inverse cosecant of \( x \). Notice that \( \csc^{-1}(x) \) is the inverse cosecant function, which implies that we are considering the angle whose cosecant value is \( x \). We assume that \( x \) is appropriately defined, meaning that it satisfies the domain restrictions for the inverse cosecant function, \( x \geq 1 \) or \( x \leq -1 \), excluding 0.
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