Inverse Trigonometric Functions
Addition of Inverse Tangents
Premium Question
Grade 12
Question:
If $\tan^{-1} \frac{1}{2} + \tan^{-1} \frac{1}{5} + \tan^{-1} \frac{1}{8} = \frac{\pi}{k}$, find $k$.
Step-by-Step Solution
Key Concept: Combine $\tan^{-1}(1/2) + \tan^{-1}(1/5)$ first (check $1/2 \cdot 1/5 < 1$). Then add $\tan^{-1}(1/8)$ to the result and recognise the answer.
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Correct Answer: 4