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In a triangular \(\rm \cos\frac{(A+B)}{2}=\) ______

This question was previously asked in
Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 2)
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  1. \(\rm \cos \frac{c}{2}\)
  2. \(-\rm \sin \frac{c}{2}\)
  3. \(\rm \cos\left(\frac{A-B}{2}\right)\)
  4. \(\rm \sin \frac{c}{2}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \sin \frac{c}{2}\)
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Detailed Solution

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Calculations:

In a Triangle A + B + C = 180° 

A + B = 180° - C

\(\rm \cos\frac{(A+B)}{2}=\)  Cos((180 - C)/2) = Cos(90° - C/2) = Sin(C/2)

Hence, The Correct Answer is \(\rm \sin \frac{c}{2}\).

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