If `A+B+C+D=360^(@)`, the prove that `cos 2A + cos 2B + cos 2C + cos 2D =4 cos (A+B) cos (A+C) cos (A+D) `

If A + B + C =pi , prove that : cos 2A + cos 2B + cos 2C = -1-4 cos A cos B cos C .

If A+B+C=0 , then prove that cos ^(2)A+ cos ^(2) B + cos ^(2) C =1+2 cos A cos B cos C

If A + B + C = (pi)/(2) , prove that cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B cos C

If A+B +C +D= 2 pi , prove that : cos A + cos B + cos C + cos D =-4 cos frac (A+B)(2) cos frac (A+C)(2) cos frac (A+D)(2) .

If A + B + C = 180^(@) , prove that cos A + cos B - cos C = -1 + 4 cos (A)/(2) cos"" (B)/(2) sin"" (C )/(2)

If A + B + C + D = 2pi , prove that: cos A + cos B + cos C + cos D =-4"cos"(A+B)/(2)"cos"(A+C)/(2)"cos"(A+D)/(2)

If A+B+C=pi , prove that cos 2A +cos 2B +cos 2C=-1-4cos A cos Bcos C.

If A+B+C=pi , prove that cos 2A +cos 2B +cos 2C=-1-4cos A cos Bcos C.

If A+B+C = pi prove that cos 4A + cos 4B + cos 4C = -1 + 4 cos 2A cos 2B cos 2C