If a,b,c,d are in G.P., then prove that: `(b-c)^2 + (c-a)^2+(d-b)^2=(a-d)^2`

If a,b,c,d are in proportion, then prove that (a^2+ab+b^2)/(a^2-ab+b^2)=(c^2+cd+d^2)/(c^2-cd+d^2)

If a,b,c,d are in proportion, then prove that (11a^2+9ac)/(11b^2+9bd)=(a^2+3ac)/(b^2+3bd)

If a,b,c,d are in proportion, then prove that sqrt((a^2+5c^2)/(b^2+5d^2))=a/b

If a/b =b/c and a,b, c gt 0 , then prove that (a+b)^2/(b+c)^2 = (a^2 +b^2)/(b^2 +c^2)

If x -iy = frac{a-ib}{c-id} , then prove that ( x^2 + y^2 ) = frac{a^2+b^2}{c^2+d^2}

If (a+ib)(c+id)(e+if)(g+ih) = A+ iB, then show that ( a^2 + b^2 ) ( c^2 + d^2 )( e^2 + f^2 )( g^2 + h^2 )= ( A^2 + B^2 )

If sin theta + cos theta =a, and sin theta - cos theta =b, then ..... (A) a^2 + b^2 =1 (B) a^2 - b^2 = 1 ( C) a^2 + b^2 =2 (D) a^2 - b^2 =2

If A =[{:(a, b), (c, d):}] " then " A^(-1) = ____. a) (1)/(ad-bc)[(b,-c),(-d,a)] b) (1)/(ab-cd)[(b,-c),(-d,a)] c) (1)/(ab-cd)[(b,d),(c,a)] d)None of these

If x-iy = sqrt (frac{a-ib}{c-id}) , prove that (x^2+y^2) = frac{a^2+b^2}{c^2+d^2}