Prove $\tan \left( x + \frac { \pi } { 4 } \right) = \frac { 1 + \tan x } { 1 - \tan x }$

question 112

Essay

Prove $\tan \left( x + \frac { \pi } { 4 } \right) = \frac { 1 + \tan x } { 1 - \tan x }$ .

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Definitions:

Penalty Kick

A method of restarting play in soccer, awarded for a foul within the penalty area, taken from the penalty spot against only the goalkeeper.

Kicker's Payoffs

A rephrased definition: The potential returns or outcomes that a participant in a game or negotiation, known as the "kicker," stands to gain.

Probability of Success

The likelihood of a particular outcome deemed favorable or meeting a set goal.

Probability of Failure

The likelihood or risk that a system, component, or process will fail to perform within an expected timeframe.