Home
Class 11
MATHS
If cos e cA+secA=cos e c B+s e cB , prov...

If `cos e cA+secA=cos e c B+s e cB ,` prove that: `"tanAtanB"=cot(A+B)/2`

Text Solution

Verified by Experts

Given:--
`cos e cA+secA=cos e c B+s e cB ,`
`=>cosecA−cosecB=secB−secA`
`=>1/(sinA)−1/(sinB)=1/(cosB)−1/(cosA)`
`=>(sinB−sinA)/(sinA.sinB)=(cosA−cosB)/(cosA.cosB)`
`=> (2sin(B−A)/2cos(B+A)/2)/(sinA.sinB)=(2sin(B−A)/2sin(B+A)/2)/(cosA.cosB)`
`=>(cos(B+A)/2)/(sin(B+A)/2)=(sinA.sinB)/(cosA.cosB)`
`=>cot(B+A)/2=tanA.tanB`
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

Similar Questions

Explore conceptually related problems

If "cosec"A + secA="cosec"A+secB , prove that: tanA.tanB=cot(A+B)/(2)

If A+B+C= pi and cos A=cos B. cosC,prove that cot B cot C= 1/2

If cos(A+B)sin(C+D)=cos(A-B)sin(C-D) , prove that cot A cot B cot C=cotD .

If three angles A,B, and C are in A.P.prove that: cot B=(s in A-s in C)/(cos C-cos A)

If a_1, a_2, a_n are in A.P. with common difference d!=0 , then the sum of the series sind[seca_1seca_2+(sec)_2seca_3+....+s e ca_(n-1)(sec)_n] is : a.cos e ca_n-cos e ca b. cota_n-cota c. s e ca_n-s e ca d. t a na_n-t a na

The expression (t a n A)/(1-cot A)+(cot A)/(1-t a n A) can be written as sin A cos A+1 b. s e c A\ cos e c A+1 c. t a n A+cot A d. s e c A+cos e c A

If a,b and c be in A.P. prove that cos A cot((A)/(2)),cos B cot((B)/(2)), and cos C cot((C)/(2)) are in A.P.

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), ...

    Text Solution

    |

  2. If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y...

    Text Solution

    |

  3. If cos e cA+secA=cos e c B+s e cB , prove that: "tanAtanB"=cot(A+B)/2

    Text Solution

    |

  4. If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma...

    Text Solution

    |

  5. If cos A+cosB=1/2 and sin A+ sinB=1/4 , prove that: tan((A+B)/2)=1/2

    Text Solution

    |

  6. If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(2pi)/3) , prove that...

    Text Solution

    |

  7. If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany...

    Text Solution

    |

  8. Prove that: tan20^0tan40^0tan80^0=tan60^0

    Text Solution

    |

  9. Prove that :"sin"Asin(60^0-A)sin(60^0+A)=1/4sin3A

    Text Solution

    |

  10. Show that: t a n(60^0+theta)t a n(60^0-theta)=(2cos2theta+1)/(2cos2the...

    Text Solution

    |

  11. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

    Text Solution

    |

  12. Prove that: cos20^0cos40^0cos60^0cos80^0=1/(16)

    Text Solution

    |

  13. Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)

    Text Solution

    |

  14. Prove that: 4"cos"12^0cos48^0cos72^0=cos36^0

    Text Solution

    |

  15. Prove that: t a nthetatan(60^0-theta)tan(60^0+theta)=tan3thetadot

    Text Solution

    |

  16. Prove that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

    Text Solution

    |

  17. If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= (a)2sin3x (...

    Text Solution

    |

  18. Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B...

    Text Solution

    |

  19. Prove that: ((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n=...

    Text Solution

    |

  20. If sintheta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/...

    Text Solution

    |