Home
Class 9
MATHS
Prove that : (a^(-1))/(a^(-1)+b^(-1))+(a...

Prove that : `(a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(b^2-a^2)`

Text Solution

AI Generated Solution

To prove the equation \[ \frac{a^{-1}}{a^{-1} + b^{-1}} + \frac{a^{-1}}{a^{-1} - b^{-1}} = \frac{2b^2}{b^2 - a^2} \] we will simplify the left-hand side step by step. ...
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    RD SHARMA|Exercise All Questions|23 Videos

  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA|Exercise All Questions|226 Videos

Similar Questions

Explore conceptually related problems

Prove that (i) (a^(-1))/(a^(-1) + b^(-1)) + (a^(-1))/(a^(-1)-b^(-1)) = (2b^(2))/(b^(2) -a^(2)) (ii) (1)/(1+x^(a-b)) + (1)/(1+x^(b-a)) = 1

Prove that 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

Prove that : cos ^(-1) ((1- a^(2))/(1+a)) + cos ^(-1)((1-b^(2))/(1+b^(2))) = 2 tan ^(-1) .(a+b)/(1-ab)

Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

if a,b,c are in H.P., prove that ((1)/(a)+(1)/(b)-(1)/(c))((1)/(b)+(1)/(c)-(1)/(a))=(4)/(ac)-(3)/(b^(2))

det[[ Prove that :,c^(2)a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),[c-1)^(2)]]=4det[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

Prove that: tan^(-1){(pi)/(4)+(1)/(2)(cos^(-1)a)/(b)}+tan{(pi)/(4)-(1)/(2)(cos^(-1)a)/(b)}=(2b)/(a)

If a,b, and c are in G.P.then prove that (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

If a, b, c are in geometric progression, then prove that : (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

If a, b, c are in G.P., then prove that (1)/(a^(2)-b^(2))-(1)/(b^(2)-c^(2))=-(1)/(b^(2)) . [Hint : Put b = ar, c = ar^(2) ]

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that : (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/...

    Text Solution

    |

  2. Find the value of x , if 5^(x-3). 3^(2x-8)=225

    Text Solution

    |

  3. Show that : (x^(a(b-c)))/(x^(b(a-c)))*(x^b)/(x^a))^c=1 ((x^(a+b))...

    Text Solution

    |

  4. If (9^nxx3^2xx(3^(-n/2))^(-2)-(27)^n)/(3^(3m)xx2^3)=1/(27), Prove th...

    Text Solution

    |

  5. If 27^x=9/(3^x), find xdot

    Text Solution

    |

  6. Find the values of x in each of the following : (i)2^(5x)-:2^x=(root(...

    Text Solution

    |

  7. Evaluate each of the following: (i)5^2*5^4 (ii) 5^8+5^3 (iii) (3...

    Text Solution

    |

  8. Evaluate each of the following: (i)(2/(11))^4*((11)/3)^2*(3/2)^3 (ii...

    Text Solution

    |

  9. If a=2 and b=3, then find the values of each of the following: a^a+b^b...

    Text Solution

    |

  10. Assuming that x , y are positive real numbers, simplify each of the fo...

    Text Solution

    |

  11. Simplify : ((25)^(3/2)x(243)^(3/5))/((16)^(5/4)x(8)^(4/3))

    Text Solution

    |

  12. Simplify: ((81)/(16))^(-3/4)xx[((25)/9)^(-3/2)-:(5/2)^(-3)]

    Text Solution

    |

  13. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

    Text Solution

    |

  14. Evaluate each of the following 5^2\xx\ 5^4 (ii) (3^2)^3 ​ ​ ​

    Text Solution

    |

  15. Evaluate each of the following (i)((11)/(12))^3 (ii) (3/4)^(-3)

    Text Solution

    |

  16. Evaluate each of the following: (i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)...

    Text Solution

    |

  17. Evaluate each of the following: (i)\ 2^(55)xx\ 2^(60)-\ 2^(97)xx\ 2^(...

    Text Solution

    |

  18. If a=2 and b=3 , then find the values of each of the following: a^a+b^...

    Text Solution

    |

  19. If a=2 and b=3 , then find the values of each of the following: (a/b)^...

    Text Solution

    |

  20. Simplify the following (ii)(3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(18 ...

    Text Solution

    |