Current location - Training Enrollment Network - Mathematics courses - Senior high school mathematics compulsory 5
Senior high school mathematics compulsory 5
It is proved that (1) is derived from cosine theorem in triangle,

cosA=(b^2+c^2-a^2)/2bc,

Because a, b and c are three sides of a triangle, they cannot be negative numbers.

Because 0, that is, (b 2+c 2-a 2)/2bc > 0...* formula.

Multiply both sides of * by 2bc,

So b 2+c 2-a 2 > 0, and then move the

a^2<; b^2+c^2

Proof of the original proposition.

(2) In triangle, it is obtained by cosine theorem.

cosA=(b^2+c^2-a^2)/2bc,

Because a, b and c are three sides of a triangle, they cannot be negative numbers.

And because ∠A is an obtuse angle,

Therefore, COSA < 0, that is, (b 2+c 2-a 2)/2bc < 0...* formula.

Multiply both sides of * by 2bc,

So b 2+c 2-a 2 < 0, and then move the

a^2>; b^2+c^2

Proof of the original proposition