Inverse Trigonometric Functions
Machin's Formula
Premium Question
Grade 12
Question:
Find the integer value of $\tan[4 \tan^{-1} \frac{1}{5} - \tan^{-1} \frac{1}{239}]$.
Step-by-Step Solution
Key Concept: Apply the double-angle formula twice to find $4 \tan^{-1}(1/5)$. Then subtract using the $\tan^{-1}$ subtraction formula. This is a famous identity.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 1