`sin^2(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)`

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

If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

If A+B-C=3pi, t h e n sin A+ sin B-sin C is equal to- a.4sin(A/2)sin(B/2)cos(C/2) b. -4sin(A/2)sin(B/2)cos(C/2) c. 4cos(A/2)cos(B/2)cos(C/2) d. -4cos(A/2)cos(B/2)cos(C/2)

If A+B+C=180^(@), then prove that cos^(2)(A)/(2)+cos^(2)(B)/(2)+cos^(2)(C)/(2)=2(1+sin(A)/(2)sin(B)/(2)sin(C)/(2))

If A+B+C=180^0 , prove that : cos^2( A/2) + cos^2( B/2) + cos^2(C/2) = 2+2 sin(A/2) sin( B/2) sin( C/2)

In DeltaABC , prove that: sin^(2)A+sin^(2)B+sin^(2)C =1-cos^(2)A+sin^(2)B+1-cos^(2)C =2-cos(A+B)cos(A-B)-cos^(2)C =2-cos(180^(@)-C)cos(A-B)-cosC.coc{180^(@)-(A+B)} =2+cosC.cos(A-B)+cos(A+B)] =2+cosC.2cosAcosB =RHS Hence proved.

If : A+B+C= pi "then" : 1 - sin^(2)""(A)/(2) - sin^(2)""(B)/(2)+ sin^(2)""(C)/(2)= A) 2cos""(A)/(2) * cos sin ^(2)""(B)/(2) + sin^(2)""(C)/(2) B) 2 cos ""(B)/(2)* cos ""(B)/(2) * sin""(C)/(2) C) 2 cos ""(C)/(2)* cos ""(A)/(2) * sin""(B)/(2) D) 2 cos ""(A)/(2)* cos ""(B)/(2) * sin""(C)/(2)

If the sides a,b and C of o+ABC are in A.P.,prove that 2sin(A)/(2)sin(C)/(2)=sin(B)/(2)a cos^(2)(C)/(2)+cos^(2)(A)/(2)=(3b)/(2)

If : A+B+C=pi, "then"" "sin ^(2) A +sin^(2)B - sin ^(2)C= A) 2 cos A * cos B * sin C B) 2 cos B * cos C * sin A C) 2 sin A * sin B * cos C D) 2 sin B * sin C * cos A

In Delta ABC If,(sin^(2)A+sin^(2)B+sin^(2)C)/(cos^(2)A+cos^(2)B+cos^(2)C)=2 Then the triangle is