Track / Stage 4 / 273 of 340 #533 of 1964
Problem 533 AMC 12 late, AIME early Difficulty 4.9 Prove it
In △ A B C \triangle A B C △ A B C ( a − b ) 2 cos 2 C 2 + ( a + b ) 2 sin 2 C 2 = c 2 .
(a-b)^{2} \cos ^{2} \frac{C}{2}+(a+b)^{2} \sin ^{2} \frac{C}{2}=c^{2} .
( a − b ) 2 cos 2 2 C + ( a + b ) 2 sin 2 2 C = 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
Next problem →
Official solution 6. After reducing the order, remove the parentheses, and then use the cosine rule.
← Previous All problems Next →
Source: NuminaMath-1.5 ,
licensed Apache-2.0 .
Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.