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20 10 who can quickly solve the last question of Jiangsu college entrance examination mathematics (the problem is below)!
The first question is proved by cosine theorem 2bcosa = b 2+c 2-a 2, which is said upstairs.

The second question is proved by induction, because when n = 1, cosnA is a rational number, right?

So let's assume that coskx is a rational number. Now let's prove that cos(k+ 1)x is also a rational number.

According to the sum angle formula, it looks simple. . .

Cos (k+1) x = cos (kx+x) = coskxcosx-sinksinx are all rational numbers, because the four operation results of rational numbers are still rational numbers, which is the basic theorem of rational numbers.

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