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

Verified by Experts

The correct Answer is:
214
Promotional Banner

Topper's Solved these Questions

  • INDICES [EXPONENTS]

    ICSE|Exercise EXERCISE 7 (B)|29 Videos

  • INDICES (EXPONENTS)

    ICSE|Exercise 4 Marks Questions|9 Videos

  • INEQUALITIES

    ICSE|Exercise EXERCISE 11|42 Videos

Similar Questions

Explore conceptually related problems

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

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

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

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then, (a) a_(1)/a_(2)=b_(1)/b_(2) (b) a_(1)a_(2)=b_(1)b_(2) (c) a_(1)a_(2)+b_(1)b_(2)=0 (d) a_(1)-a_(2)=b_(1)-b_(2)

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

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

Prove that : tan [(pi)/(4) + (1)/(2) cos^(-1)""(a)/(b)] + tan[(pi)/(4) - (1)/(2) cos^(-1)""(a)/(b)] = (2b)/(a) .

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Using properties of determinants, prove that: |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|=(1+a^(2)+b^(2))^(3)

In DeltaABC , prove that: (1+cosA.cos(B-C))/(1+cosC.cos(A-B))=(b^(2)+c^(2))/(a^(2)+b^(2))

ICSE-INDICES [EXPONENTS]-EXERCISE 7 (C)
  1. Evaluate : 9^((5)/(2)) - 3xx8^(0)-((1)/(81))^(-(1)/(2))

    Text Solution

    |

  2. Evaluate : (64)^((2)/(3))-root(3)(125)-(1)/(2^(-5))+(27)^(-(2)/(3))...

    Text Solution

    |

  3. Evaluate : [(-(2)/(3))^(-2)]^(3)xx((1)/(3))^(-4)xx3^(-1)xx(1)/(6)

    Text Solution

    |

  4. Simplify : (3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

    Text Solution

    |

  5. Solve : 3^(x-1)xx5^(2y-3)=225.

    Text Solution

    |

  6. If ((a^(-1)b^(2))/(a^(2)b^(-4)))div((a^(3)b^(-5))/(a^(-2)b^(3)))=a^(x)...

    Text Solution

    |

  7. If 3^(x +1) = 9^(x - 3), find the value of 2^(1 + x).

    Text Solution

    |

  8. If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value o...

    Text Solution

    |

  9. If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27) , prove that m...

    Text Solution

    |

  10. Solve for x : x:(13)^sqrt(x)=4^(4)-3^(4)-6.

    Text Solution

    |

  11. If 3^(4x)=(81)^(-1)and(10)^((1)/(y))=0.0001, value of 2^(-x) xx 16^(y)...

    Text Solution

    |

  12. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

    Text Solution

    |

  13. If (a^(m))^(n)=a^(m).a^(n), find the value of : m(n - 1) - (n - 1)

    Text Solution

    |

  14. If m = root(3)(15) and n = root(3)(14), find the value of m - n - (1)/...

    Text Solution

    |

  15. Evaluate : (2^(n)xx6^(m+1)xx10^(m-n)xx15^(m+n-2))/(4^(m)xx3^(2m+n)xx25...

    Text Solution

    |

  16. Evaluate : ((x^(q))/(x^(r )))^((1)/(qr))xx((x^(r ))/(x^(p)))^((1)/(rp)...

    Text Solution

    |

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

    Text Solution

    |

  18. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

    Text Solution

    |

  19. Evaluate : (4)/((216)^(-2//3))+(1)/((256)^(-3//4))+(2)/((343)^(-1//3)...

    Text Solution

    |