Question

1-cos2a/2+1-cos2b/2+1-cos2c/2=1-2sina/2 sinb/2 sinc/2

Answer 1

A+B+C = pai

Dividing by 2 on both sides

C/2 = pi/2 - (A/2+B/2)

sin^2 A/2 +sin^2 B/2 + sin^2 C/2 

=1- Cos^2 A/2 +sin^2 B/2 + sin^2 C/2 

=1- [Cos^2 A/2 -sin^2 B/2] + sin^2 C/2 

=1- Cos((A+B)/2 Cos (A-B)/2 + sin^2 C/2 

=1- Cos(pi/2 -C/2) Cos (A-B)/2 + sin^2 C/2

=1- Sin C/2 Cos (A-B)/2 + sin^2 C/2

=1- Sin C/2 [Cos (A-B)/2 - sin C/2]

=1- Sin C/2 [Cos (A-B)/2 - sin [pi/2 - (A/2+B/2)]]

=1- Sin C/2 [Cos (A-B)/2 -Cos (A/2+B/2)]

=1- Sin C/2 [2Sin A/2 Sin B/2]

=1-2SinA/2 Sin B/2 Sin C/2

Answer 2

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