Math

If A+B+C=pi then prove that cos3A. cos3B+cos3B. cos3C+cos3C. cos3A=1

Step-by-step explanation:

Given:

A+B+C = π

3A+3B+3C = 3π

cos (3A+3B) = - cos3C

cos3A. cos3B-sin3A. sin3B = - cos3C

cos3A. cos3B = sin3A. sin3B - cos3C (1)

similarly apply for the other two angles, we have:

cos3B. cos3C = sin3B. sin3C - cos3A (2) cos3C. cos3A = sin3C. sin3A - cos3B (3)

Grouping three equations, (1) + (2) + (3), we have:

cos3A. cos3B+cos3B. cos3C+cos3C. cos3A = sin3A. sin3B + sin3B. sin3C + sin3C. sin3A - (cos3A + cos3B + cos3C)

= 1

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