What is the value of +B/2+C/2+A/2 ? [NDA I 2016]

Correct Answer is : None of the above

Correct Answer is : None of the above

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NDA Math Trigonometric Ratios of Angles and Equations

For the next two (2) items that follow :

Consider a triangle ABC in which

\cos A + \cos B + \cos C = \sqrt{3} \sin \frac{\pi}{3}

[NDA I 2016]

Question : 63 of 100

Marks: +1, -0

What is the value of

\cos\frac{A+B}{2}\cos\frac{B+C}{2}\cos\frac{C+A}{2}

Solution:

As we know that

\sin\;\;\frac{A}{2}\sin\;\;\frac{B}{2}\sin\;\;\frac{C}{2}=\;\;\frac{1}{8}

\because\left(\;\;\frac{A+B}{2}=\;\;\frac{\pi}{2}-\;\;\frac{C}{2}\right)

\therefore\cos\left(\;\;\frac{A+B}{2}\right)\cos\left(\;\;\frac{B+C}{2}\right)\cos\left(\;\;\frac{C+A}{2}\right)=\;\;\frac{1}{8}

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