Home
Class 12
MATHS
If A,B,C, are the angles of a triangle s...

If A,B,C, are the angles of a triangle such that `cotA/2=3tanC/2,` then `sinA ,sinB ,sinC` are in `AdotPdot` (b) `GdotPdot` (c) `HdotPdot` (d) none of these

A

AP

B

GP

C

HP

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
Given `cot((A)/(2))cot((C)/(2))=3`
`rArr (cos((A)/(2))cos((C)/(2)))/(sin((A)/(2))sin((C)/(2)))=3`
`rArr(cos((A-C)/(2)))/(cos((A+C)/(2)))=2`
`rArr 2sinB=sinA+sinC`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If A, B, C are the angles of a triangle such that sin^(2)A+sin^(2)B=sin^(2)C , then

If cos2B=(cos(A+C))/("cos"(A-C)) , then tanA ,t a n B ,tanC are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If A ,Ba n dC are the vetices of a triangle A B C , then prove sine rule a/(sinA)=b/(sinB)=c/(sinC)dot

If all the vertices of a triangle have integral coordinates, then the triangle may be (a) right-angled (b) equilateral (c) isosceles (d) none of these

If A,B,C are angles of a triangle, then 2sin(A/2)cosec (B/2)sin(C/2)-sinAcot(B/2)-cosA is (a)independent of A,B,C (b) function of A,B (c)function of C (d) none of these

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, and C=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

In a /_\A B C , if tanA/2,tanB/2,tanC/2"are in"AdotPdot, then show that cosA ,cosB ,cosC are in AdotPdot

If A,B,C are the angles of a non right angled triangle ABC. Then find the value of: |[tanA,1,1],[1,tanB,1],[1,1,tanC]|

In a triangle ABC, if sinAsin(B-C)=sinCsin(A-B), then prove that cotA ,cotB ,cotC are in AdotPdot

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If sintheta1sintheta2-costheta1costheta2+1=0, then the value of tan((t...

    Text Solution

    |

  2. The value of expression (2(sin1^0+sin2^0+sin3^0++sin89^0)/(2(cos1^0+co...

    Text Solution

    |

  3. If A,B,C, are the angles of a triangle such that cotA/2=3tanC/2, then ...

    Text Solution

    |

  4. If 2sec 2theta=tan phi+cotphi, then one of the values of theta+phi is

    Text Solution

    |

  5. The roots of the equation 4x^2-2sqrt(5)x+1=0,a r e sin36^0,sin18^0 (...

    Text Solution

    |

  6. If Aa n dB are acute positive angles satisfying the equations 3sin^2A+...

    Text Solution

    |

  7. If cos 25^0 + sin 25^0 = p, then cos 50^0 is equal to

    Text Solution

    |

  8. The value of cot(7pi)/(16)+2cot(3pi)/8+cot(15pi)/(16) is 4 (b) 2 (c...

    Text Solution

    |

  9. If alpha,beta,gamma,delta are the smallest positive angles in ascendin...

    Text Solution

    |

  10. (sin^2A-sin^2B)/(sinAcosA-sinBcosB)i se q u a lto "tan"(A-B) (b) ...

    Text Solution

    |

  11. If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2...

    Text Solution

    |

  12. The value of cos^2 10^0-cos10^0cos50^0+cos^2 50^0 is equal to 4/3 (b)...

    Text Solution

    |

  13. If tan^2theta=2tan^2varphi+1,t h e ncos2theta+sin^2varphi equals -1 (...

    Text Solution

    |

  14. If sinx+cos e cx+tany+coty=4 where x and y in [0,pi/2],then tan(y/2) i...

    Text Solution

    |

  15. If 2 sin 2alpha=tan beta,alpha,beta, in((pi)/(2),pi), then the value o...

    Text Solution

    |

  16. If 2|sin2alpha|=tanbeta+cotbeta|,alpha,beta in (pi/2pi), then the valu...

    Text Solution

    |

  17. The value of sin^3 10^0+sin^3 50^0-sin^3 70^0 is equal to -3/2 (b) 3/...

    Text Solution

    |

  18. Let P(x)=((1-cos2x+sin2x)/(1+cos2x+s in2x))^2+((1+cotx+cot^2x)/(1+tanx...

    Text Solution

    |

  19. If (3-tan^2pi/7)/(1-tan^2pi/7)=kcospi/7 then the value of k is 1 (b) 2...

    Text Solution

    |

  20. cos e c(360^0)/7+cos e c(540^0)/7= cos e c(180^0)/7 (b) cos e c(90^0...

    Text Solution

    |