Home
Class 12
MATHS
Let P={theta:sintheta-costheta=sqrt2cos...

Let `P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+costheta=sqrt2sintheta}` be two ses. Then,

A

`Q notinP`

B

`P notinQ`

C

`P sub Q and Q-P ne phi`

D

`P=Q`

Text Solution

Verified by Experts

The correct Answer is:
D
Let Q `in` P. Then,
`thetainPhArrsin theta-costheta=sqrt2costheta`
`hArr1-2sinthetacostheta=2cos^(2)theta`
`hArr2 sin thetacos theta=2 cos^(2)theta`
hArr`1+2sin thetacos theta=2-2 cos^(2)theta`
`hArr(sin theta+cos theta)^(2)=2 sin ^(2)theta`
`hArr sintheta+cos theta=sqrt2sintheta`
`hArrtheta in Q.`
hence, `P =Q.`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Exercise|190 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

Let P={theta:sintheta-costheta=sqrt2costheta}and Q={theta: sintheta+costheta=sqrt2sintheta} be two sets. Then

If sintheta+costheta=sqrt(2)sintheta , then sintheta-costheta=?

If sin theta+costheta=sqrt(2)costheta then what is (costheta-sintheta) equal to ?

If costheta-sintheta=sqrt(2)costheta , then find the value of costheta+sintheta .

If : cos theta-sintheta=sqrt2.sin theta, "then": costheta+sintheta=

If costheta+sintheta=sqrt(2)costheta , then costheta-sintheta is

If sintheta - cos theta = sqrt(2)cos theta , then the value of sintheta + cos theta is:

If costheta +sin theta= sqrt(2)cos theta , then prove that costheta-sintheta =sqrt(2)sin theta

int((sintheta+costheta))/sqrt(sin2theta)"d"theta=

If sintheta+costheta=sqrt(2)sin(90^(@)-theta) , then cottheta=?

OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. If a=sinxcos^3x and b=cosxsin^3x then

    Text Solution

    |

  2. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as

    Text Solution

    |

  3. Let P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+c...

    Text Solution

    |

  4. If xcosalpha+ysinalpha=xcosbeta+ysinbeta=2a, then cosalpha cosbeta=

    Text Solution

    |

  5. If sin theta+cosec theta=2, "then the volume of" sin ^(10)theta+cosec...

    Text Solution

    |

  6. The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^...

    Text Solution

    |

  7. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  8. If sin(theta+alpha)=a,cos^(2)(alpha+beta)=b, then sin(alpha-beta)=

    Text Solution

    |

  9. Len n be an odd integer. If sinn theta=sum(r=0)^(n) b(r)sin^(r)theta f...

    Text Solution

    |

  10. Which one of the following number (s) is/are rational?

    Text Solution

    |

  11. Let (3pi)/4 < theta < pi and sqrt(2 cot theta+1/sin^2 theta) = k - cot...

    Text Solution

    |

  12. The values of sum(k=1)^(13) (1)/(sin((pi)/(4)+(k-1)(pi)/(6))sin((pi)/(...

    Text Solution

    |

  13. If A > 0, B > 0 and A+B=pi/6, then the minimum value of tan A + tan B ...

    Text Solution

    |

  14. For a positive integer n , fn(theta)=(tantheta/2)(1+sectheta)(1+sec2th...

    Text Solution

    |

  15. Let f(theta)=sintheta(sintheta+sin3theta).Then, f(theta)

    Text Solution

    |

  16. If alpha+beta=pi/2 and beta+gamma=alpha then tanalpha equals

    Text Solution

    |

  17. If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is

    Text Solution

    |

  18. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

  19. The maximum value of (cosalpha(1))(cosalpha(2))...(cosalpha(n)), under...

    Text Solution

    |

  20. The value of tan (pi/16)+2tan(pi/8)+4 is equal to

    Text Solution

    |