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If A+B+C=pi, prove that tan^2A/2+tan^2B/...

If `A+B+C=pi,` prove that `tan^2A/2+tan^2B/2+tan^2C/2geq1.`

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To prove that \( \tan^2 \frac{A}{2} + \tan^2 \frac{B}{2} + \tan^2 \frac{C}{2} \geq 1 \) given that \( A + B + C = \pi \), we can follow these steps: ### Step 1: Use the identity for tangent of half angles We start by using the identity for the tangent of half angles: \[ \tan \frac{A}{2} = \sqrt{\frac{1 - \cos A}{1 + \cos A}}, \quad \tan \frac{B}{2} = \sqrt{\frac{1 - \cos B}{1 + \cos B}}, \quad \tan \frac{C}{2} = \sqrt{\frac{1 - \cos C}{1 + \cos C}} \] ...
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