Prove That
2sin^2A + 2sin^2B + 2sin^2C = 2sin^2A + 1 - cos2B + 1 - cos2C
2sin²A +2sin²B+2sin²C =2sin²A+1-cos2B+1-cos2C
sin²B = (1/2)(1-cos2B) identity
2sin²B = 1-cos2B
sin²C =(1/2)(1-cos2C) identity
2sin²C =1-cos2C
2sin²A+2sin²B+2sin²C = 2sin²A+1-cos2B+1-cos2C
hence approved!
Comments
2sin²A +2sin²B+2sin²C =2sin²A+1-cos2B+1-cos2C
sin²B = (1/2)(1-cos2B) identity
2sin²B = 1-cos2B
sin²C =(1/2)(1-cos2C) identity
2sin²C =1-cos2C
2sin²A+2sin²B+2sin²C = 2sin²A+1-cos2B+1-cos2C
hence approved!