Question

If \[ \frac{\tan(A-B)}{\tan A}+\frac{\sin^2 C}{\sin^2 A}=1, \quad A,B,C\in\left(0,\frac{\pi}{2}\right), \] then:

• A. \( \tan A, \tan B, \tan C \) are in G.P.
• B. \( \tan A, \tan C, \tan B \) are in G.P.
• C. \( \tan A, \tan B, \tan C \) are in A.P.
• D. \( \tan A, \tan C, \tan B \) are in A.P.

Hint:

In trigonometric problems involving \( A+B+C=\frac{\pi}{2} \), always try converting everything into tangents for faster conclusions.

Answer 1

The Correct Option is A