If `a^4+b^4+c^4+a^2b^2=2c^2(a^2+b^2)`,, then show that`angleC=60^@or120^@`

If a^(4) + b^(4) + c^(4) + a^(2)b^(2) = 2c^(2)(a^(2) + b^(2)) then show that, C=60^(@) or 120^(@)

If in triangleABC ,a^4+b^4+c^4=2c^2(a^2+b^2) then find angleC

(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^(@)

If a^(4) + b^(4) = 14 a^(2)b^(2) , then show that log(a^(2) + b^(2)) = log a + log b + 2 log 2 .

In triangle ABC if a^(4) + b^(4) + c^(4) = 2a^(2)b^(2) + 2b^(2)c^(2) then the values of B will be-

If a, b, c are the sides of the triangle ABC such that a^(4) +b^(4) +c^(4)=2x^(2) (a^(2)+b^(2)), then the angle opposite to the side c is-

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^@

If a sinx = b cos x = (2c tan x)/(1-tan^2 x) then show that (a^2-b^2)=4c^2(a^2+b^2) .

If (5a-3b)/a= (4a+b-2c)/(a+4b-2c) = (a+2b-3c)/(4a-4c) , then show that 6a=4b=3c.

a,b,c are the lengths of sides of triangleABC and 1/(a+c)+1/(b+c)=3/(a+b+c),show that angleC=60^@