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If A+B+C=180^0, prove that : cos^2 (A/2)...

If `A+B+C=180^0`, prove that : `cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) = 2cos (A/2) cos (B/2) sin (C/2)`

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AI Generated Solution

To prove the identity \( \cos^2 \left( \frac{A}{2} \right) + \cos^2 \left( \frac{B}{2} \right) - \cos^2 \left( \frac{C}{2} \right) = 2 \cos \left( \frac{A}{2} \right) \cos \left( \frac{B}{2} \right) \sin \left( \frac{C}{2} \right) \) given that \( A + B + C = 180^\circ \), we can follow these steps: ### Step 1: Use the given condition Since \( A + B + C = 180^\circ \), we can express \( C \) in terms of \( A \) and \( B \): \[ C = 180^\circ - (A + B) \] ...
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