[" Question "58],[" In a "/_ABC,sin^(4)A+sin^(4)B+sin^(4)C=]

In a Delta ABC, sin ^(4) A + sin ^(4) B + sin ^(4) C =

(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^(@)

Prove that in a ABC,sin^(2)A+sin^(2)B+sin^(2)C<=(9)/(4)

In Delta ABC, sin A: sin B: sin C is

In a /_ABC,sin^(4)A+sin^(4)B+sin^(4)C=(3)/(2)+2cos A cos B cos C+(1)/(2)cos2A cos2B cos2C

If 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, if sin^(2)A + sin^(2)B + sin^(2)C = 9/4 , show that the triangle is equilateral.

In Delta ABC , if sin ^(2)A +sin ^(2) B +sin ^(2) C =(3)/(4) , then the triangles is