" If "2(a^(2)+b^(2))=(a+b)^(2)" ,then show that "a=b

If sin alpha=(a^(2)-b^(2))/(a^(2)+b^(2)) , then show that cot alpha=(2ab)/(a^(2)-b^(2)) .

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 .

If a^(2),b^(2),c^(2) are in A.P,then show that: b+c-a,c+a-b,a+b-c are in A.P.

If (a^(2) + b^(2))sin (A-B) = (a^(2)-b^(2)) sin(A+B) then show that, the triangle is either isoscelels or right angled.

If (a+c):(b+c) = (a/b+2):(b/a+2) then show that (a-c):(b-c) = a^2:b^2 .

If a^(2),b^(2),c^(2) are in A.P,show that: (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P.

If x= (sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b)) , then show that bx^2-ax+b=0

If (a+b+c)(a-b+c)=a^2+b^2+c^2 then show that a,b,c are in continued proportion.

If (A^2+B^2 ) prop (A^2-B^2) then show that A prop

If a,b,quad >0 such that a^(3)+b^(3)=2, then show that a+b<=2.