Track / Stage 4 / 245 of 340 #505 of 1964

6. In $\triangle A B C$, prove:
$$(a-b)^{2} \cos ^{2} \frac{C}{2}+(a+b)^{2} \sin ^{2} \frac{C}{2}=c^{2} .$$

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Official solution

6. After reducing the order, remove the parentheses, and then use the cosine rule.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.