In a ΔABC, if \(\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k\) , then k is always
We can put values of the angles \(A\), \(B\), and \(C\) to get an idea about the value of \(k\): 1. Put \(A = B = C = 60^\circ\): \[ k = \tan^2 30^\circ + \tan^2 30^\circ + \tan^2 30^\circ = 1 \] 2. Put another set of values \(A = B = 30^\circ\) and \(C = 120^\circ\): \[ k = \tan^2 15^\circ + \tan^2 15^\circ + \tan^2 45^\circ > 1 \] Hence, \(k \geq 1\).
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