Question

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

Answer 1

Answer:

Step-by-step explanation:

A+B+C = pi,

A+B+C = π,

3A+3B+3C = 3π,

cos(3A+3B) = - cos3C,

cos3A.cos3B-sin3A.sin3B = - cos3C,

cos3A.cos3B = sin3A.sin3B  - cos3C,

similarly,

cos3B.cos3C = sin3B.sin3C  - cos3A,

cos3C.cos3A = sin3C.sin3A  - cos3B,

adding the 3 equations,

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

= 1.

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