Prove that: `sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-D) = 0`

Show that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that (cos^(2)A-sin^(2)B)+1-cos^(2)C

Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C

In a DeltaA B C ,\ prove that , sin^3Acos(B-C)+sin^3B cos(C-A)+sin^3\ C cos(A-B) = 3\ sin A\ sin B \ sin C

If A+B+C=pi , prove that : (sin ((B+C)/(2)) + sin ((C+A)/(2)) + sin( (A+B)/(2) )) equals (4cos ((pi-A)/(4)) cos( (pi-B)/(4)) cos((pi-C)/(4))) .

Prove that: ("sin"(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+("sin"(C-A))/(cos C cos A)=0