Prove that : Question on Trignometry

cosx+cosy+cosz+cos[x+y+z] = 4 cos(x+y)/2cos(y+z)/2cos(z+x)/2

Dear student,

There can be many ways to prove this equality. one such way is as follows:
Keep the Numerator as it is.
Start with the denominator. Multilpy and divide the LHS by 2 and Apply 2CosACosB formula to the denominator.
Do the above step once more to obtain 4 cos terms in addition which will be same as the numerator term . Numerator and denomator shall cancel out leaving behind a 4 in the numerator as a factor which is equal to RHS