[" Prove that: "],[sin^(2)A sin A cos A cos^(2)A],[sin^(2)B sin B cos B cos^(2)B],[sin^(2)C sin C cos C cos^(2)C]=-sin(A-B)sin(B-C)sin(C-A)

If A+B+C = pi , show that |["sin"^(2)A, "sin A cos A", "cos"^(2)A],["sin"^(2) B, "sin B cos B", "cos"^(2)B],["sin"^(2)C, "sin C cos C", "cos"^(2)C]| =-"sin (A-B)"sin"(B-C)"sin"(C-A)"

If A+B+C=pi, prove that sin^(2)A+sin^(2)B+sin^(2)C=2(1+cos A cos B cos C)

If A+B+C=pi , prove that sin 2A+sin 2B-sin 2C=4 cos A cos B sin C

(2sin (AC) cos C-sin (A-2C)) / (2sin (BC) cos C-sin (B-2C)) = (sin A) / (sin B)

(2sin (AC) cos C-sin (A-2C)) / (2sin (BC) cos C-sin (B-2C)) = (sin A) / (sin B)

Prove that sin(A+B+C)=sin A cos B cos C+cos A sin B cos C+cos A cos B sin C-sin A sin B sin Ccos(A+B+C)=cos A cos B cos C-cos A sin B sin C-sin A cos B sin C-sin A sin B cos C

prove that , |{:(sin A ,cos A,sin (A+theta)),(sin B ,cos B,sin (B+theta)),(sin C ,cos C ,sin (C+theta)):}|=0

Prove that a cos A + b cos B + c cos C = 4R sin A sin B sin C

If A+B+C= (pi)/(2) ,prove that: (i) cos^(2)A+cos^(2)B+cos^(2)C=2+2"sin"A "sin"B "sin"C (ii) "sin"^(2)+"sin"^(2)B+"sin"^(2)C=1-2 "sin"A sin B sin C .

Prove that : (sin 2A+sin 2B + sin 2C)/(cos A + cos B + cos C-1) = 8 cos(A/2) cos( B/2) cos( C/2)