Home
Class 11
MATHS
alpha is a root of the equation (2sinx-c...

`alpha` is a root of the equation `(2sinx-cosx)(1+cosx)=sin^2x`
`beta` is a root of the equation `3cos^2x-10cosx+3=0` and `gamma` is a root of the equation 1-sin2x=cosx-sinx where `0 le alpha, beta, gamma le pi//2`
Answer the following question on above passage:
`sin(alpha-beta)`

A

1

B

0

C

`(1-2sqrt6)/6`

D

`(sqrt3-2sqrt2)/6`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos

  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 and gamma is a root of the equation 1-sin2x=cosx-sinx where 0 le alpha, beta, gamma le pi//2 Answer the following question on above passage: sinalpha+sinbeta+singamma can be equal

if 0ltalpha,beta,gamma lt(pi/2) prove that sin alpha+sin beta+sin gamma gtsin(alpha+beta+gamma)

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

The roots of the equation x^2+3x+4=0 are alpha and beta .Form the equations whose roots are (alpha+beta)^2 and (alpha-beta)^2

Let alpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta the roots of the equation x^2-12x+b=0 . If alpha,beta,gamma and delta are in G.P. having positive common ratio, then find the values of a and b.

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and betadot

If alpha,beta,gamma are the roots of the equation x^3+x+1=0 , then the value of alpha^3+beta^3+gamma^3 is.

If alpha , beta , gamma are the roots of the equation px^3 - qx + r = 0 , then the value of alpha + beta + gamma is

If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of the equation x^2-ax+b=0 be alpha,1/beta then prove that, bq(a-p)^2=(q-b)^2 .

If the roots of the equation ax^2+bx+c=0 be alpha and beta , find the equation whose roots are alpha+alpha^2/beta and beta+beta^2/alpha

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. Let f(x)=e^(cos^-1sin(x+pi/3)), then

    Text Solution

    |

  2. The greatest and least values of (sin^-1x)^3+(cos^-1x)^3 are

    Text Solution

    |

  3. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  4. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  5. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |

  6. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |

  7. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

    Text Solution

    |

  8. sum(r=1)^ntan^-1((xr-x(r-1))/(1+x(r-1)xr))=sum(r=1)^n(tan^-1xr-tan^-1x...

    Text Solution

    |

  9. Arrange the followig radicals in increasing order of -I effect. 1,Br,C...

    Text Solution

    |

  10. Match Column-I with Column-II

    Text Solution

    |

  11. The number of values of theta in the interval (-pi/2, pi/2) such that ...

    Text Solution

    |

  12. If a, b, c, d in (0, pi) and b+c ne pi/2 such that 2cosa+6cosb+7cosc+9...

    Text Solution

    |

  13. The value of 1/2{sec^2(tan^-1 2)+cosec^2(cot^-1 3)+tan^2(pi/3)} is equ...

    Text Solution

    |

  14. If x gt 0, then the value of sin{tan^-1((1-x^2)/(2x))+cos^-1((1-x^2)/(...

    Text Solution

    |

  15. If cos^-1(x/2)+sin^-1(x/4)=pi/6, then the value of x is

    Text Solution

    |

  16. Solve: cos^4(x/5)+sin^2(x/5)=1

    Text Solution

    |

  17. Solve: abscot(2x-pi/2)=1/(cos^2 2x)-1

    Text Solution

    |

  18. Solve: 2cos^2x+5cosx+2 ge 0

    Text Solution

    |

  19. Find the points of intersection of the curves y=cosx and y=sin3x if -p...

    Text Solution

    |

  20. Solve for x and y : 2^(1/cos^2x)sqrt(y^2-y+1//2) le 1

    Text Solution

    |