Home
Class 12
MATHS
Prove that 2tan^(-1)(sqrt((a-b)/(a+b))ta...

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

Text Solution

AI Generated Solution

To prove the equation \[ 2\tan^{-1}\left(\sqrt{\frac{a-b}{a+b}} \tan\left(\frac{\theta}{2}\right)\right) = \cos^{-1}\left(\frac{a \cos \theta + b}{a + b \cos \theta}\right), \] we will follow a systematic approach using trigonometric identities and properties of inverse functions. ...
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 2 tan^(-1) (sqrt((a-b)/(a+b)) "tan"(theta)/(2))=cos^(-1) ((a cos theta +b)/(a +b cos theta))

The value 2tan^(-1)[sqrt((a-b)/(a+b)tantheta/2)] is equal to cos^(-1)((acostheta+b)/(a+bcostheta)) (b) cos^(-1)((a+bcostheta)/(acostheta+b)) cos^(-1)((acostheta)/(a+bcostheta)) (d) cos^(-1)((bcostheta)/(acostheta+b))

The value 2tan^(-1)[sqrt((a-b)/(a+b))tantheta/2] is equal to cos^(-1)((acostheta+b)/(a+bcostheta)) (b) cos^(-1)((a+bcostheta)/(acostheta+b)) cos^(-1)((acostheta)/(a+bcostheta)) (d) cos^(-1)((bcostheta)/(acostheta+b))

If a , b , c >0 and s=(a+b+c)/2 , prove that tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

Prove that ("tan"^(2)theta)/(("sec"theta-1)^(2))=(1+"cos"theta)/(1-"cos"theta) .

Prove that : (tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =' pi'

Prove that : tan^(-1)( (2a-b)/(bsqrt(3))) +tan^(-1)((2b-a)/(asqrt(3))) = pi/3

Prove that tan ^(-1) ""(1)/(4) + tan ^(-1) ""(2)/(9) = cos ^(-1) ((2)/(sqrt5))

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

RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Write the value of sin{pi/3-sin^(-1)(-1/2)}

    Text Solution

    |

  2. If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot

    Text Solution

    |

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

    Text Solution

    |

  4. Solve the following equation for x : tan^(-1)(1/4)+2tan^(-1)(1/5)+...

    Text Solution

    |

  5. Write the value of cos^2(1/2cos^(-1)3/5)

    Text Solution

    |

  6. Write the value of sin^-1(sin1550^@)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(...

    Text Solution

    |

  12. Write the following functions in the simplest form: tan^(-1){x/(sqrt...

    Text Solution

    |

  13. Evaluate each of the following: cot^(-1)(1/(sqrt(3)))-cos e c^(-1)(-2)...

    Text Solution

    |

  14. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

    Text Solution

    |

  15. Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqr...

    Text Solution

    |

  16. Evaluate each of the following: sin^(-1)(sinpi/3) (ii) cos^(-1)(cos(2...

    Text Solution

    |

  17. If cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2, find the value ...

    Text Solution

    |

  18. For the principal values, evaluate the following: tan^(-1)sqrt(3)-se...

    Text Solution

    |

  19. Find the principal values of cot^(-1)sqrt(3) and cot^(-1)(-1)

    Text Solution

    |

  20. For the principal values, evaluate the following: sin^(-1)(-(sqrt(3))...

    Text Solution

    |