If A+B+C=180^(@), prove that (i) sin 2A+sin 2B+sin 2C=4 sin A sin B sin C (ii) cos A+cos B-Cos C=-1 +4 cos ""A/2 cos ""B/2sin ""C/2 (iii) sin^(2) A+sin^(2) B+sin^(2) C=2+2 cos A cos B cos C (iv) sin^(2) A+sin^(2) B-sin^(2) C=2 sin A sin B cos C (v) tan ""A/2 tan""B/2 +tan""B/2 tan ""C/2+tan ""C/2 tan""A/2=1 (vi) sin A+sin B+ sin C=4 cos ""A/2 cos""B/2 cos ""C/2 (viii) sin (B+C-A) +sin (C+A-B) +sin (A+B-C)=4 sin A sin B sin C.

If A+B+C=180^(@), prove that (i) sin 2A+sin 2B+sin 2C=4 sin A sin B s

1.	If A+B+C=180^(@), prove that (i) sin 2A+sin 2B+sin 2C=4 sin A sin B sin C (ii) cos A+cos B-Cos C=-1 +4 cos ""A/2 cos ""B/2sin ""C/2 (iii) sin^(2) A+sin^(2) B+sin^(2) C=2+2 cos A cos B cos C (iv) sin^(2) A+sin^(2) B-sin^(2) C=2 sin A sin B cos C (v) tan ""A/2 tan""B/2 +tan""B/2 tan ""C/2+tan ""C/2 tan""A/2=1 (vi) sin A+sin B+ sin C=4 cos ""A/2 cos""B/2 cos ""C/2 (viii) sin (B+C-A) +sin (C+A-B) +sin (A+B-C)=4 sin A sin B sin C.
Answer» Answer :(i) `4 sin A sin B sin C` (ii) `-1+4 COS""A/2 cos ""B/2 sin ""C/2` (iii) `2+2 cos A cos B cos C` (iv) `2 sin A sin B cos C` (v) 1 (vi) `4 sin A sin B sin C`