Question

The solution set of the equation \[ x \in \left(0,\frac{\pi}{2}\right), \quad \tan(\pi \tan x) = \cot(\pi \cot x) \] is:

• A. \( \{0\} \)
• B. \( \left\{\frac{\pi}{4}\right\} \)
• C. \( \varnothing \)
• D. \( \left\{\frac{\pi}{6}\right\} \)

Hint:

For mixed tan/cot equations: Convert cot to tan.  Use symmetry in \( (0,\frac{\pi}{2}) \).

Answer 1

The Correct Option is B