Home
Class 11
MATHS
For n in Z , the general solution of (s...

For `n in Z ,` the general solution of `(sqrt(3)-1)sintheta+(sqrt(3)+1)costheta=2 is(n in Z)` `theta=2npi+-pi/4+pi/(12)` `theta=npi+(-1)^npi/4+pi/(12)` `theta=2npi+-pi/4` `theta=npi+(-1)^npi/4-pi/(12)`

Text Solution

Verified by Experts

`(sqrt3-1)sintheta+(sqrt3+1)costheta=2`
`((sqrt3-1)/(2sqrt2))sintheta+((sqrt3+1)/(2sqrt2))costhe ta=2/(2sqrt2`
`sinpi/12sintheta+cospi/12costheta=cospi/7`
`cos(theta-pi/7)=cospi/4`
`theta-pi/2=2npipmpi/4`
`theta=2npipmpi/4+pi/12`.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

A general solution of tan^2theta+cos2theta=1 is (n in Z) npi=pi/4 (b) 2npi+pi/4 npi+pi/4 (d) npi

3tan(theta - pi/12) = tan(theta + pi/12)

One of the general solutions of sqrt(3) cos theta-3 sin theta=4 sin 2 theta cos 3 theta is mpi+pi/(18),m in Z (mpi)/2+pi/6,AAm in Z m pi/3+pi/(18),m in Z none of these

sqrt(3)tantheta tan(theta + pi/3) tan(theta + (2pi)/3) =1

costheta - sintheta = 1/sqrt(2) (-pi lt theta lt pi)

One of the general solutions of 4sinthetasin2thetasin4theta=sin3theta is (3n+-1)pi/(12),AAn in Z (4n+-1)pi/9,AAn in Z (3n+-1)pi/(12),AAn in Z (3n+-1)pi/3,AAn in Z

The general solution of the equation sinx-3sin2x+sin3x=cosx-3cos2x+cos3x is (n in Z) npi+pi/8 (b) (npi)/2+pi/8 (-1)^n(npi)/2+pi/8 (d) 2npi+cos^(-1)2/3

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Show that the following two equations represent the same set of angles: theta - pi/6 = 2npi +-pi/3 and theta + pi/3 = npi + (-1)^(n) pi/6

The general solution of the trigonometric equation sinx+cosx=1 is given by x=2npi,n0,+-1,+-2 x=2npi+pi/2; n=0,+-1,+-2, dot x=npi+(-1)^npi/4-pi/4n=0,+-1,+-2, non eoft h e s e

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If tantheta+sectheta=1. 5 , find sintheta,tantheta and secthetadot

    Text Solution

    |

  2. Show that the line joining the incenter to the circumcenter of triangl...

    Text Solution

    |

  3. For n in Z , the general solution of (sqrt(3)-1)sintheta+(sqrt(3)+1)c...

    Text Solution

    |

  4. The value of cot70^0+4cos70^0 is

    Text Solution

    |

  5. In A B C , right-angled at C , if tanA=sqrt((sqrt5-1)/2) , show tha...

    Text Solution

    |

  6. If "coses"theta-sintheta=m,sectheta-costheta=n,"eliminate"theta

    Text Solution

    |

  7. The solution of 4sin^2x+tan^2x+cos e c^2x+cot^2x-6=0i s(n in Z) (a) ...

    Text Solution

    |

  8. The value of sin (pi/14)sin(3pi/14)sin(5pi/14)sin(7pi/14)sin(9pi/14)si...

    Text Solution

    |

  9. If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

    Text Solution

    |

  10. In A B C , if (sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c...

    Text Solution

    |

  11. The set of values of x satisfying the equation sin3alpha=4sinalphasin(...

    Text Solution

    |

  12. cos e c(360^0)/7+cos e c(540^0)/7

    Text Solution

    |

  13. If (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC)...

    Text Solution

    |

  14. In a triangle A B C , the altitude from A is not less than B C and the...

    Text Solution

    |

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

    Text Solution

    |

  16. If tan(A-B)=1a n dsec(A+B)=2/(sqrt(3)) , then the smallest positive va...

    Text Solution

    |

  17. Prove that sqrt((1+sintheta)/(1-sintheta))=sectheta+tantheta

    Text Solution

    |

  18. If in A B C ,A C is double of A B , then the value of cot(A/2)cot((B-...

    Text Solution

    |

  19. If 3tan(theta-15^0)=tan(theta+15^0), then theta is equal to n in Z)

    Text Solution

    |

  20. Let P(x)=((1-cos2x+sin2x)/(1+cos2x+sin2x))+((1+cotx+cot^2x)/(1+tanx+ta...

    Text Solution

    |