`(b^(2)-a^(2))-(a^(2)-b^(2))=`

Simplify ((a^(2)+b^(2))/(a^(2)-b^(2))-(a^(2)-b^(2))/(a^(2)+b^(2)))/((a+b)/(a-b)-(a-b)/(a+b))

If a, b, c are in G.P. , then show that (i) (a^(2) - b^(2))(b^(2) + c^(2)) = (b^(2) -c^(2)) (a^(2) + b^(2)) (ii) a( b^(2) + c^(2)) = c (a^(2) + b^(2))

If : sin theta = (a^(2)-b^(2))/(a^(2)+b^(2)), "then" : cot theta= A) (4a^(2)b^(2))/(a^(2) -b^(2)) B) (a^(2) + b^(2))/(a^(2) - b^(2)) C) (4a^(2)b^(2))/(a^(2) + b^(2)) D)none of these.

If tan theta=(a)/(b), then (a sin theta+b cos theta)/(a sin theta-b cos theta) is equal to (a^(2)+b^(2))/(a^(2)-b^(2))(b)(a^(2)-b^(2))/(a^(2)+b^(2))(c)(a+b)/(a-b)(d)(a-b)/(a+b)

Area of the quadrilateral formed with the foci of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1( a) 4(a^(2)+b^(2))( b) 2(a^(2)+b^(2))( c) (a^(2)+b^(2))(d)(1)/(2)(a^(2)+b^(2))

Simplify: (a^(2)-(b-c)^(2))/((a+c)^(2)-b^(2))+(b^(2)-(a-c)^(2))/((a+b)^(2)-c^(2))+(c^(2)-(a-b)^(2))/((b+c)^(2)-a^(2))

If cos theta+sin theta=a,cos2 theta=b, then (a)a^(2)=b^(2)(2-a^(2))(b)b^(2)=a^(2)(2-b^(2))(c)b^(2)=a^(2)(2-a^(2))(d)a^(2)=b^(2)(2-b^(2))

Prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

Simplify the following algebraic expressions : a^(2) - [b^(2) - {a^(2)-(2b^(2)- bar(a^(2)+b^(2)) }]

Simplify the following expression and then find its value when a = 2 and b = - 1 : 2(a^(2) - b^(2)) - [ 2a^(2) - { b^(2) - (a^(2)+b^(2) +ab)}]