Question

If \(x=\tan A, y=\tan B, z=\tan C\) and \[ xy+yz+zx=1, \] then evaluate \[ \frac{(1-x^2)(1-y^2)(1-z^2)}{(1+x^2)(1+y^2)(1+z^2)} \]

• A. \(\frac{4xy}{(1+x^2)(1+y^2)}\)
• B. \(4xyz\)
• C. \(\frac{4xy}{(1+x^2)(1+y^2)}+\frac{2z}{1+z^2}\)
• D. \(1\) \bigskip

Hint:

Whenever \(xy+yz+zx=1\) for tangents, it often implies \(A+B+C=\frac{\pi}{2}\).

Answer 1

The Correct Option is D