Prove: CosA+CosB+CosC=4.Sin(A/2).Sin(B/2).Sin(C/2)+1.

Let's first apply your observation to sin(C/2), along with the angle difference and sum formulas for sine, and the angle sum formula for cosine.Read more

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We will use the angle sum property of the triangle to answer this question. Answer: cos A + cos B + cos C = 1 + 4 sin(A/2) sin(B/2) sin(C/2)Read more

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I could start a semi-proof by using limits: as A→0,cosAcosBcosC becomes big (as we want), but A+B+C becomes too small. Also, as A→π2 ...Read more

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The minimum value of cos a + cos b + cos c is 1, which occurs when one of the angles is zero. If you don't like the idea of triangles having angles which are 0,Read more

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cos a + cos b + cos c + cos (a+b+c) =2 cos ((a+b)/2) cos ((ab)/2) + 2 cos ((c+a+b+c)/2) cos ((ca-b+c)/2) Read more

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If cosA+cosB+cosC=0,then show that cos3A+cos3B+cos3C=12cosAcosB cosC Mathematical Ecstasy.Read more

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To prove that cos ⁡ A + cos ⁡ B + cos ⁡ C = 1 + r R , where A , B , C are the angles of a triangle, r is the inradius, and R is the circumradius, ...Read more

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The vertices of triangle ABC are A(1,3), B(7,7) and C(9,3) and I need to find the orthocenter.Read more

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