Home
Class 12
MATHS
If tan beta=2sin alpha sin gamma co sec(...

If `tan beta=2sin alpha sin gamma co sec(alpha+gamma)`, then `cot alpha,cot beta,cotgamma` are in

A

AP

B

GP

C

HP

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
`tan beta=22sin alpha sin gamma co sec (alpha+gamma)=(2sin alpha sin gamma)/(sin(alpha+gamma))`
or `cos beta=(sin(alpha+gamma))/(2sin alpha sin beta)`
or `2 cot beta=(sin alpha cos gamma+cos alpha sin gamma)/(sin alpha sin gamma)=cot alpha+cot gamma`
or `cot alpha,cot beta, cot gamma` are in AP.
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 cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that cos 3alpha + cos 3 beta + cos gamma = 3 cos (alpha + beta + gamma) and

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .

If cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2 alpha + 2 tan^2 alpha tan^2 beta tan^2 gamma = 1 then sin^2 alpha + sin^2 beta + sin^2 gamma =

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat k ,cos(alpha-beta) hat i+ hat j+"cos"(gamma-beta) hat ka n dcos(alpha-gamma) hat i+cos(beta-gamma) hat k+a hat k where alpha,beta , and gamma are different angles. If these vectors are coplanar, show that a is independent of alpha,beta and gamma

If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha beta gamma beta gamma alpha gamma alpha beta|=0,alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha,a n dgamma+alpha-betadot

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If cos2B=(cos(A+C))/("cos"(A-C)), then tanA ,t a n B ,tanC are in A.P....

    Text Solution

    |

  2. If ("cos"(x-y))/("cos"(+y))+("cos"(z+t))/(cos(z-t))=0 , then the value...

    Text Solution

    |

  3. If tan beta=2sin alpha sin gamma co sec(alpha+gamma), then cot alpha,c...

    Text Solution

    |

  4. the value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

    Text Solution

    |

  5. If cos^3xsin2x=sum(r=0)^n axsin(r x),AAx in R then

    Text Solution

    |

  6. cos^6pi/9-33tan^4pi/9+27tan^2pi/9 is equal to 0 (b) sqrt(3) (c) 3 ...

    Text Solution

    |

  7. Given that a , b , c , are the side of a A B C which is right angled ...

    Text Solution

    |

  8. If theta=3alphaa n dsintheta=a/(sqrt(a^2+b^2)), the value of the expre...

    Text Solution

    |

  9. tan 6^@ . Tan 42^@. Tan 66^@ . Tan 78^@ is

    Text Solution

    |

  10. In triangle A B C , if angle c is 90 and the area of triangle is 30 s...

    Text Solution

    |

  11. If sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A...

    Text Solution

    |

  12. In a right angled triangle the hypotenuse is 2sqrt(2) times the perpen...

    Text Solution

    |

  13. A circular ring of radius 3cm hangs horizontally form a point 4cm v...

    Text Solution

    |

  14. The distance between the two parallel lines is 1 unit. A point A is ch...

    Text Solution

    |

  15. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then asqrt(1-a^2)+bsqrt(1-b^2)+cs...

    Text Solution

    |

  16. If A+B+C=(3pi)/2, t h e ncos2A+cos2B+cos2C is equal to 1-4cos Acos Bc...

    Text Solution

    |

  17. If tan(alpha+beta)=(sin2beta,)/(3-cos2beta) then tanalpha=2tanbeta (b...

    Text Solution

    |

  18. In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to 2sinAsi...

    Text Solution

    |

  19. The value of sum(r=0)^(10)cos^3(rpi)/3 is equal to 1/4 (b) 1/8 (c) -...

    Text Solution

    |

  20. In triangle A B C ,(sinA+sinB+sinC)/(sinA+sinB-sinC) is equal to tanA/...

    Text Solution

    |