Calculating Tan 2 X And Introducing Cot X

graph TB; A["Calculating tan (?/2-x) and introducing cot x"] --> B["Step 1: Understand the Problem"]; A --> C["Step 2: Identify the Knowns"]; A --> D["Step 3: Identify the Unknowns"]; B --> E["Step 1.1: Break Down the Problem"]; C --> F["Step 2.1: List the Knowns"]; D --> G["Step 3.1: List the Unknowns"]; E --> H["Step 1.2: Understand the Formula"]; F --> I["Step 2.2: Apply the Knowns"]; G --> J["Step 3.2: Solve for the Unknowns"]; H --> K["Step 1.3: Understand tan and cot"]; I --> L["Step 2.3: Substitute the Knowns into the Formula"]; J --> M["Step 3.3: Solve the Equation"]; K --> N["Step 1.4: Understand the Relationship between tan and cot"]; L --> O["Step 2.4: Simplify the Equation"]; M --> P["Step 3.4: Check the Solution"];