Question

If a=3, b=4, c=5 then cosA/2=​

Answer 1

Answer:

We know that Cos A =

$\frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} = \frac{ {4}^{2} + {5}^{2} - {3}^{2} }{2 \times 4 \times 5} = \frac{32}{8 \times 5} = \frac{4}{5}$

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) =

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