Home
Class 12
MATHS
Solution of the equation sin (sqrt(1+sin...

Solution of the equation `sin (sqrt(1+sin 2 theta))= sin theta + cos theta` is `(n in Z)`

A

`n pi-pi/4`

B

`n pi+pi/12`

C

`n pi+pi/6`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`sin (sqrt(1+sin 2 theta))= sin theta + cos theta`
`rArr sin(sin theta + cos theta)= sin theta + cos theta`
The equation of the form `sin x =x`
`rArr x=0`
`rArr 1+ sin 2 theta=0`
`rArr sin 2 theta =-1`
`rArr theta=npi -pi/4, n in Z`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.9|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Solution of the equation sin(sqrt(1+sin2 theta))=sin theta+cos theta is (n in Z)n pi-(pi)/(4)(b)n pi+(pi)/(12)(c)n pi+(pi)/(6)(d) none of these

General solution of the equation (sqrt(3) - 1) sin theta + (sqrt(3) + 1) cos theta = 2 is

The solution of the equation 1-"cos" theta = "sin" theta "sin" (theta)/(2) is

The general solution of the equation sin theta + cos theta = 1 is theta =

If cos theta+sin theta=sqrt(2)sin theta then sin theta-cos theta is

General solution of the equation sin^(3) theta cdot cos theta - sin theta cdot cos^(3) theta = 1//4 is theta =

The general solution of the equation sin theta=cos theta is

The solution of the equation cos^(2)theta-2cos theta=4sin theta-sin2 theta where theta in[0,pi] is

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

Find the general value of theta which satisfies the equation (cos theta+i sin theta)(cos2 theta+i sin2 theta)......(cos n theta+i sin n theta)=1

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. The number of solution of sin^(4)x-cos^(2) x sin x+2 sin^(2)x+sin x=0 ...

    Text Solution

    |

  2. The range of 'y, such that the equation in x, y + cos x = sin x has a ...

    Text Solution

    |

  3. Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos th...

    Text Solution

    |

  4. One of the general solutions of sqrt(3) cos theta -3 sin theta =4 sin ...

    Text Solution

    |

  5. The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//s...

    Text Solution

    |

  6. (sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqr...

    Text Solution

    |

  7. For 0<x , y<pi, the number of ordered pairs (x , y) satisfying the sys...

    Text Solution

    |

  8. The least positive solution of cot (pi/(3 sqrt(3)) sin 2x)=sqrt(3) lie...

    Text Solution

    |

  9. The number of real roots of the equation cosec theta + sec theta-sqrt(...

    Text Solution

    |

  10. If =lt=xlt=2pi, then the number of solutions of 3(sinx+cosx)-(sin^3x+c...

    Text Solution

    |

  11. If 2 sin^(2) ((pi//2) cos^(2) x)=1-cos (pi sin 2x), x ne (2n + 1) pi//...

    Text Solution

    |

  12. The number of solutions of the equation cos6x+tan^2x+cos6xtan^2x=1 in ...

    Text Solution

    |

  13. The number of solutions of the equation sin^3xcosx+sin^2xcos^2x+sinxco...

    Text Solution

    |

  14. The sum of all the solution of the equation costhetacos(pi/3+theta)cos...

    Text Solution

    |

  15. General solution of sin^(2) x-5 sin x cos x -6 cos^(2)x=0 is

    Text Solution

    |

  16. The total number of solution of sin^(4)x+cos^(4) x= sin x cos x in [0,...

    Text Solution

    |

  17. General solution of tan theta+tan 4 theta+tan 7 theta=tan theta tan 4 ...

    Text Solution

    |

  18. The general solution of tan theta+tan 2 theta+tan 3 theta=0 is

    Text Solution

    |

  19. The number of solution of sec^(2) theta + cosec^(2) theta+2 cosec^(2) ...

    Text Solution

    |

  20. Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e ...

    Text Solution

    |