Home
Class 10
MATHS
If tanA+sinA=m and tanA-sinA=n, then pro...

If `tanA+sinA=m and tanA-sinA=n`, then prove that `m^(2)-n^(2)=4sqrt(mn)`.

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|66 Videos

  • THEOREMS RELATED TO TANGENT IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 4.2|23 Videos

  • TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|28 Videos

Similar Questions

Explore conceptually related problems

If sinA=sinB and cosA=cosB , then prove that sin((A-B)/2)=0

If tan theta+sin theta=m and tan theta-sin theta=n , prove that, mn=tan^2sin^2theta and m^2-n^2=4sqrt(mn)(mgtn) .

If " cosec"theta-sin theta=m and sec theta-cos theta=n , then prove that (m^(2)n)^((2)/(3))+(mn^(2))^((2)/(3))=1.

If tanA+sinA=p and tanA-sinA=q , then which one of the following is correct ?

If tan A =ntanB , sinA =msinB , prove that , cos^2A=(m^2-1)/(n^2-1) .

If tanA=5/6 and tanB=1/(11) , Prove that A+B=pi/.4

If sinx+cosx=m and secx+cosecx=n prove that n(m^2-1)=2m

Answer any Two questions : In triangle ABC angle C = 90^@ , If BC = m and AC = n then prove that m sin A+ n sin B = sqrt(m^2+ n^2)

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be m:n, then prove that p^(2)mn=q(m+n)^(2) .

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4

CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. Prove that (sin A+sinB)/(cosB-cosA)=(cos A+cosB)/(sinA-sinB).

    Text Solution

    |

  2. Prove that (sec theta-tan theta+1)/(sec theta+tan theta+1)=(1-sin the...

    Text Solution

    |

  3. Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha...

    Text Solution

    |

  4. If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3), then ...

    Text Solution

    |

  5. eliminate theta : a(1) sec theta + b(1)tan theta+c(1)=0 , a(2)sec thet...

    Text Solution

    |

  6. If tan theta=(a)/(b) , then find the value of (sin theta)/(cos^(8)thet...

    Text Solution

    |

  7. If a^(2)sec^(2)alpha-b^(2)tan^(2)alpha=c^(2), then prove that sinalpha...

    Text Solution

    |

  8. If tan theta=k, then show that sec theta+tan^(3)theta "cosec"theta=(1...

    Text Solution

    |

  9. If tan^(2)theta=1-e^(2), then prove that sectheta+tan^(3)theta"cosec...

    Text Solution

    |

  10. If " cosec"theta-sin theta=m and sec theta-cos theta=n, then prove tha...

    Text Solution

    |

  11. If a sin x=b cosx=(2c tan x)/(1-tan^(2)x), then prove that (a^(2)-b^(...

    Text Solution

    |

  12. If (sin alpha-cosalpha)/(sin alpha+cosalpha)=tan theta, then prove tha...

    Text Solution

    |

  13. If (cos^(4)alpha)/(cos^(2)beta)+(sin^(4)alpha)/(sin^(2)beta)=1, then ...

    Text Solution

    |

  14. If u(n)=sin^(n)alpha+cos^(n)alpha, then prove that 2u(6)-3u(4)+1=0.

    Text Solution

    |

  15. If theta be a positive acute angle and tan theta=(a)/(b), then find th...

    Text Solution

    |

  16. If tanA+sinA=m and tanA-sinA=n, then prove that m^(2)-n^(2)=4sqrt(mn)...

    Text Solution

    |

  17. If k tan theta=tan k theta, then prove that (sin^(2)k theta)/(sin^(2)...

    Text Solution

    |

  18. If c cos^(3)theta+3c cos theta sin^(2)theta=m and c sin^(3)theta+3c c...

    Text Solution

    |

  19. If x=r cos theta cos phi, y=r cos theta sin phi, z=r sin theta, then p...

    Text Solution

    |

  20. If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta, th...

    Text Solution

    |