If sin A/sin C=sin(A-B)/sin(B-C) then show that `a^2,b^2,c^2` are in arithmetic progression

If (sin A)/(sin C) = (sin (A-B))/(sin (B-C)) , then show that, a^(2), b^(2), c^(2) are in A.P.

If 2 cos A = (sin B)/(sin C) then show that the triangle is isosceles.

In any triangle ABC if sin A sin B sin C+ cos A cos B=1 , then show that a:b:c=1:1: sqrt(2) .

If in triangleABC ,sin^4A+sin^4B+sin^4C=sin^2Bsin^2C+2sin^2Csin^2A+2sin^2Asin^2B then show that angle A is either 30^@ or 150^@

(i) If in a triangle ABC, a^(4) + b^(4) +c^(4) - 2b^(2) c^(2) -2c^(2)a^(2)=0 , then show that, C=45^(@) or 135^(@) . (ii) In in a triangle ABC, sin^(4)A + sin^(4)B + sin^(4)C = sin^(2)B sin^(2)C + 2sin^(2) C sin^(2)A + 2sin^(2)A sin^(2)B , show that, one of the angles of the triangle is 30^(@) or 150^(@)

In any triangle ABC show that b^2sin2C+c^2sin 2B=abc/R

In triangle ABC if sin^2B+sin^2C=sin^2A then

In triangleABC,sin((B+C)/2) =

If sin^(2)B+ sin^(2)C = sin^(2)A , then the triangle ABC is-

In triangleABC sin^2A+sin^2B =sin^2C then angleC=