Home
Class 12
MATHS
Prove that : tan^(-1){(cos2\ alphasec2\ ...

Prove that : `tan^(-1){(cos2\ alphasec2\ beta+cos2betasec2alpha)/2}=tan^(-1){t a n^2(alpha+beta)t a n^2(alpha-beta)}+tan^(-1)1`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

  • LINEAR PROGRAMING

    RD SHARMA ENGLISH|Exercise All Questions|4 Videos

Similar Questions

Explore conceptually related problems

Prove that: tan^(-1){(cos2alphasec2beta+cos2betasec2alpha)/2}=tan^(-1){tan^2(alpha+beta)tan^2(alpha-beta)}+tan^(-1)1

Prove that (cos^2 alpha - cos^2 beta)/(cos^2 alpha*cos^2 beta) = tan^2 beta - tan^2 alpha

Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(-1)(tan (alpha/2) tan (beta/2))

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s e c^2(1/2tan^(-1)(beta/alpha))=(alpha+beta)(alpha^2+beta^2) .

Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec^2(1/2tan^(-1)beta/alpha)=(alpha+beta)(a^2+beta^2)dot

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

(sinalpha+sinbeta-sin(alpha+beta))/(sinalpha+sinbeta+sin(alpha+beta))=tan(alpha/2)tan(beta/2)

RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

    Text Solution

    |

  2. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s ...

    Text Solution

    |

  3. Prove that : tan^(-1){(cos2\ alphasec2\ beta+cos2betasec2alpha)/2}=tan...

    Text Solution

    |

  4. Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2...

    Text Solution

    |

  5. Evaluate the following:(i) sin(1/2\ cos^(-1)(4/5)) (ii) sin(2\ tan^...

    Text Solution

    |

  6. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

    Text Solution

    |

  7. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)=1/2s...

    Text Solution

    |

  8. Prove: tan^(-1)(2/3)=1/2tan^(-1)(12/5)

    Text Solution

    |

  9. Prove the following: tan^(-1)1/7+2\ tan^(-1)1/3=pi/4

    Text Solution

    |

  10. Prove the following : sin^(-1)(4/5)+2\ tan^(-1)(1/3)=pi/2

    Text Solution

    |

  11. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

    Text Solution

    |

  12. Prove the following: 2\ tan^(-1)(1/5)+tan^(-1)(1/8)= tan^(-1)(4/7)

    Text Solution

    |

  13. Prove the following: 2\ tan^(-1)(3/4)-tan^(-1)((17)/(31))=pi/4

    Text Solution

    |

  14. Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))

    Text Solution

    |

  15. Prove the following: 4\ tan^(-1)(1/5)-tan^(-1)(1/(239))=pi/4

    Text Solution

    |

  16. If sin^(-1)((2a)/(1+a^2))-cos^(-1)((1-b^2)/(1+b^2))=tan^(-1)((2x)/(1-x...

    Text Solution

    |

  17. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2

    Text Solution

    |

  18. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

    Text Solution

    |

  19. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

    Text Solution

    |

  20. Show that :2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is constant for xgeq1, fi...

    Text Solution

    |