(a^(-1)+b^(-1))^(-1)=(ab)/(a+b)

Prove that (a+b)^(-1)(a^(-1)+b^(-1))=(1)/(ab)

If log_(3)x=a and log_(7)x=b, then which of the following is equal to log_(21)x?ab(b)(ab)/(a^(-1)+b^(-1))(1)/(a+b)(d)(1)/(a^(-1)+b^(-1))

Prove that, tan^(-1)a+tan^(-1)b+tan^(-1)((1-a-b-ab)/(1+a+b-ab))=(pi)/(4) .

Statement 1: If the matrices,A,B,(A+B) are non-singular,then [A(A+B)^(-1)B]^(-1)=B^(-1)+A^(-1). Statement 2:[A(A+B)^(-1)B]^(-1)=[A(A^(-1)+B^(-1))B]^(-1)=[(I+AB^(-1))B]^(-1)=[(B+AB^(-1))B]^(-1)=[(B+AI)]^(-1)=[(B+A)]^(-1)=B^(-1)+A^(-1)

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

ab^(2)+(a-1)b-1

tan ^(-1)"" a+ cot ^(-1)""b=cot ^(-1) ""(b-a)/(1+ab)

Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+ca)=0 .

Prove that tan^(-1)((a-b)/(1+ab))+ tan^(-1)((b-c)/(1+bc))+tan^(-1)((c-a)/(1+ca))=0 , ab>(-1), bc>(-1), ca>(-1)

If |a|<1and|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^(2))b^(2)+(1+a+a^(2)+a^(3))b^(3)+ is (1)/((1-a)(1-b)) b.(1)/((1-a)(1-ab)) c.(1)/((1-b)(1-ab)) d.(1)/((1-a)(1-b)(1-ab))