[" 12.In triangle "ABC,C=90^(@)*" Then "(a^(2)-b^(2))/(a^(2)+b^(2))=],[" 1) "sin(A+B)quad " 2) "sin(A-B)],[" 3) "cos(A+B)quad " 4) "cos(A-B)]

In a triangle ABC if (a^(2) + b^(2))/(a^(2) - b^(2)) sin (A - B) = 1 and the triangle is not right angled, then cos (A - B) =

In any triangle ABC, (a+b)^2 sin^2 ((C )/(2))+(a-b)^2 cos^2 ((C )/(2))= .

Show that, in a triangle ABC. a^(2) = (b - c)^(2) cos^(2) (A/2) + (b + c)^(2) sin^(2) (A/2) .

In any triangle ABC,show that: 2a cos((B)/(2))cos((C)/(2))=(a+b+c)sin((A)/(2))

In Delta ABC ,(a-b)^(2)cos ^(2) (c /2) +(a+b)^(2) sin ^(2)""(c )/(2) =

Delta ABC,(a-b)^(2)cos^(2)((C)/(2))+(a+b)^(2)sin^(2)((C)/(2))=

If A+B+C=90^(@) then cos^(2)A+cos^(2)B+cos^(2)C=2+K sin A sin B sin C then K=

If A, B, C are angle of a triangle ABC, then the value of the determinant |(sin (A/2), sin (B/2), sin (C/2)), (sin(A+B+C), sin(B/2), cos(A/2)), (cos((A+B+C)/2), tan(A+B+C), sin (C/2))| is less than or equal to

Prove that in a triangle ABC , sin^(2)A - sin^(2)B + sin^(2)C = 2sin A *cos B *sin C .