Math Problem Statement

Find all values of 0 in the range 0° < X < 360° satisfying 15 cosec^2X+2 cotX = 23.

Solution

We are given the equation:

15csc⁡2X+2cot⁡X=2315 \csc^2 X + 2 \cot X = 23

We need to find the values of ( X \

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Trigonometric Equations

Formulas

cosec^2 X = 1 + cot^2 X
Trigonometric identity transformations

Theorems

Pythagorean identity for trigonometric functions
Solving trigonometric equations using identities

Suitable Grade Level

Grades 10-12

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