If, a+b+c=π
(i) prove that, sina+sinb-sinc = 4sina/2. sinb/2. cosc/2
(ii) prove that, cos^2a + cos^2b-cos^2c = 1-2sina. sinb. cos. c
(iii) prove that, cosa+cosb-cosc = -1+4cosa/2. cosb/2.sinc/2

(i)
A+B+C = pi
B+C = pi-A
sin(B+C) = sin(pi-A)
sin(B)cos(C)+cos(B)sin(C) = sin(pi)cos(A)-cos(pi)sin(A)
sin(B)cos(C)+cos(B)sin(C) = sin(A)
sin(B)cos(C) - sin(A) = -cos(B)sin(C)
(sin(B)cos(C) - sin(A))^2 = (-cos(B)sin(C))^2
sin^2(B)cos^2(C) + sin^2(A) - 2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C)
-2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A)

(ii)
cos^2(A) + cos^2(B) - cos^2(C) = 1-2*sin(A)*sin(B)*cos(C)
cos^2(A) + cos^2(B) - cos^2(C) = 1+cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(cos^2(B)sin^2(C) - sin^2(B)cos^2(C)) - sin^2(A) cos^2(A) + cos^2(B) - cos^2(C) = 1+((cos(B)sin(C))^2 - (sin(B)cos(C))^2) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(cos(B)sin(C)-sin(B)cos(C))(cos(B)sin(C)+sin(B)cos(C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(sin(C)cos(B)-cos(C)sin(B))(sin(C)cos(B)+cos(C)sin(B)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+sin(C-B)sin(C+B) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(cos(2B)-cos(2C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-1-(2cos^2(C)-1)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-1-2cos^2(C)+1) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+(1/2)*(2cos^2(B)-2cos^2(C)) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1+cos^2(B)-cos^2(C) - sin^2(A)
cos^2(A) + cos^2(B) - cos^2(C) = 1 - sin^2(A) + cos^2(B) - cos^2(C)
cos^2(A) + cos^2(B) - cos^2(C) = cos^2(A) + cos^2(B) - cos^2(C)

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