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If a=3, b=4, c=5 then cosA/2=​

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ANSWER:

We KNOW that COS A =

\frac{ {b}^{<klux>2</klux>} + {c}^{2} - {a}^{2} }{2bc} = \frac{ {4}^{2} + {5}^{2} - {3}^{2} }{2 \times 4 \times 5} = \frac{32}{8 \times 5} = \frac{4}{5}

Cos A = 2 Cos^2(A/2) - 1 = 4/5

Cos^2(A/2) =

\frac{ \frac{4}{5} + 1 }{2} = \frac{9}{10}

Cos(A/2) =

\sqrt{ \frac{9}{10} } = \frac{3}{ \sqrt{10} }


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