Question

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

Answer 1

Answer:

solved

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