sin⁡A+sin⁡B+sin⁡C=4 cos⁡(A/2)cos⁡(B/2)cos⁡(C/2), cos⁡A+cos⁡B+cos⁡C=1+ 4 sin⁡(A/2)sin⁡(B/2)sin⁡(C/2)

sin⁡A+sin⁡B+sin⁡C=4 cos⁡(A/2)cos⁡(B/2)cos⁡(C/2), cos⁡A+cos⁡B+cos⁡C=1+ 4 sin⁡(A/2)sin⁡(B/2)sin⁡(C/2)

If A, B, C are angles in a triangle, then prove that sin⁡A+sin⁡B+sin⁡C=4 cos⁡(A/2)cos⁡(B/2)cos⁡(C/2), sin⁡A+sin⁡B-sin⁡C=4 sin⁡(A/2) sin⁡(B/2) cos⁡(C/2), cos⁡A+cos⁡B+cos⁡C=1+ 4 sin⁡(A/2) sin⁡(B/2) sin⁡(C/2), cos⁡A+cos⁡B-cos⁡C=-1+ 4 cos⁡(A/2) cos⁡(B/2)sin⁡(C/2) #Trigonometry transformation formulas exercise 6(f)