Prove the Identity $$\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$$

question 143

Essay

Prove the identity.
- $$\frac { 5 \csc ^ { 2 } x + 4 \csc x - 1 } { \cot ^ { 2 } x } = \frac { 5 \csc x - 1 } { \csc x - 1 }$$

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Definitions:

Carbons

The elements that serve as the foundational building blocks in all forms of organic life, represented by the symbol C and known for its ability to form a vast number of compounds.

Acceptable Name

A valid chemical name that conforms to the rules set by the International Union of Pure and Applied Chemistry (IUPAC).

Compound

A compound is a substance made up of two or more different elements chemically bonded together in fixed proportions.

NMR Spectrum

A representation of the resonance frequencies of nuclei in a magnetic field, providing detailed information about the structure of molecules.