" (iii) "(a^(2)b-b^(2)a)^(2)

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 a,b,c,d are in G.P.prove that: (a^(2)+b^(2)),(b^(2)+c^(2)),(c^(2)+d^(2)) are in G.P.(a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.(1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(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 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))

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 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)

Verify that (a ^(2) - b ^(2)) (a ^(2) + b ^(2)) + (b ^(2) - c ^(2)) (b ^(2) + c ^(2)) + (c ^(2)-a ^(2)) + (c ^(2) + a ^(2)) = 0