Prove that- c 2 - a-b 2 cos 2 1 2 C- a-b 2 sin 2 1 2 C-

R.H.S=( a ^ 2 + b ^ 2 ) ( cos ^ 2 C 2 +sin ^ 2 C 2 #160; #160; #160; ) ab( cos ^ 2 C 2 sin ^ 2 C 2 #160; #160; #160; ) ...

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Prove that: ...

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Prove that: $c^{2} = {(a - b)}^{2} {cos}^{2} \frac{1}{2} C + {(a + b)}^{2} {sin}^{2} \frac{1}{2} C$ .

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{cos}^{2} \frac{{\frac{1}{2} (B - C)}}{{(b + c)}^{2}} + {sin}^{2} \frac{{\frac{1}{2} (B - C)}}{{(b - c)}^{2}} = \frac{1}{a^{2}}

\frac{(a + b + c)^{2}}{a^{2} + b^{2} + c^{2}} = \frac{c o t \frac{1}{2} A + c o t \frac{1}{2} B + c o t \frac{1}{2} C}{c o t A + c o t B + c o t C}

cos \frac{A}{2} = \sqrt{\frac{b + c}{2 c}}

a^{2} + b^{2} = c^{2}

cos \frac{A}{2} = \sqrt{\frac{b + c}{2 c}}

a^{2} + b^{2} = c^{2}

△ A B C

{(a - b)}^{2} {cos}^{2} \frac{C}{2} + {(a + b)}^{2} {sin}^{2} \frac{C}{2} = c^{2.}

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