Prove the Identity $$\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$$

question 129

Essay

Prove the identity.
- $$\cot ^ { 2 } x = ( \csc x - 1 ) ( \csc x + 1 )$$

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Definitions:

Beta

A measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole, with a value greater than 1 indicating higher risk and a value less than 1 indicating lower risk.

Treynor Measure

A metric for assessing the returns of an investment portfolio, adjusting for the risk taken as measured by beta.

Beta

A measure of a stock's volatility in comparison to the overall market's volatility, indicating the risk associated with investing in the stock.

Serial Correlation

The relationship between a data series and a lagged version of itself over consecutive time intervals.