If `A+B+C=pi,` show that `|(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos^2B),(sin^2C,sinCcosC,cos^2C)|=-sin(A-B)sin(B-C)sin(C-A)`

(i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(sin^(2)x,cos^(2)x,1+4sin2x):}| . (ii) Let A,B and C be the angles of triangle such that Agt=Bgt=C. Find the minimum value of Delta where Delta=|{:(sin^(2)A,sinAcosA,cos^(2)A),(sin^(2) B,sinBcosB,cos^(2)B),(sin^(2)C,sinCcosC,cos^(2)C):}| .

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)"

(sin^(2)A-sin^(2)B)/(sinAcosA-sinBcosB)=?

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

If A+B+C=pi then prove that sin2A-sin2B+sin2C=4cos A sin B cos C

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