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

Prove that: :(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))

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

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

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

If a,b,c are non-zero real numbers, then |(1,ab,(1)/(a)+(1)/(b)),(1,bc,(1)/(b)+(1)/(c)),(1,ca,(1)/(c)+(1)/(a))| is a)0 b)bc+ca+ab c) a^(-1)+b^(-1)+c^(-1) d)None of these

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)

"Tan"^(-1)(a-b)/(1+ab)+"Tan"^(-1)(b-c)/(1+bc)+"Tan"^(-1)(c-a)/(1+ca)=

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