Home
Class 11
MATHS
If sintheta+costheta=0 and theta lies i...

If `sintheta+costheta=0 and theta` lies in the fourth quadrant, find `sintheta and costheta`

Text Solution

Verified by Experts

`sintheta + cos theta = 0`
`=>(sintheta+costheta)^2 = 0`
`=>sin^2theta+cos^2theta+2sinthetacostheta = 0`
`=>1+sin2theta = 0`
`=>sin2theta = -1`
As, `theta` lies in fourth quadrant,
`:.2theta = (7pi)/2`
`=>theta = (7pi)/4`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|120 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

If sintheta+costheta=1 , then the value of sin2theta is

if sintheta-costheta=0, then the value of (sin^4theta+cos^4theta)

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

If sintheta+ costheta=1 , then find the general value of theta .

Let P = [theta : sintheta – costheta = sqrt2 costheta) andQ= {theta : sintheta + costheta = 12 sintheta} be two sets. Then:

If 3costheta-4sintheta=2costheta+sintheta , find tantheta .

If sintheta + 2 costheta=1 ,then prove that 2sintheta-costheta=2 .

If sintheta+costheta=sqrt(2)cos(90o-theta) , find cottheta .

If 3sintheta+4costheta =5 then find the value of: 4sintheta-3costheta

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

RD SHARMA ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If (3pi)/4 lt alpha lt pi, then sqrt(2cotalpha+1/(sin^2alpha)) is equ...

    Text Solution

    |

  2. If x=rsinthetacosphi,y=rsinthetasinphi and z=rcostheta, then x^2+y^2+...

    Text Solution

    |

  3. If sintheta+costheta=0 and theta lies in the fourth quadrant, find si...

    Text Solution

    |

  4. Prove that: sqrt(1-sintheta)/(1+s intheta)+sqrt((1+sintheta)/(1-s inth...

    Text Solution

    |

  5. Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

    Text Solution

    |

  6. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x)} =cot^2x

    Text Solution

    |

  7. If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+...

    Text Solution

    |

  8. If tanx=(b)/(a), then find the value of sqrt((a+b)/( a-b ))+sqrt((a-b)...

    Text Solution

    |

  9. Find the values of the following trigonometric ratios. (1) cos e c390^...

    Text Solution

    |

  10. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.

    Text Solution

    |

  11. Prove that: "sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+the...

    Text Solution

    |

  12. Prove that: sin^2pi/(18)+sin^2pi/9+sin^2(7pi)/(18)+sin^2(4pi)/9=2

    Text Solution

    |

  13. If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A...

    Text Solution

    |

  14. Find the value of the expression 3{sin^4((3pi)/2-theta)+sin^4(3pi+the...

    Text Solution

    |

  15. If t a n^2theta=1-a^2 , prove that sectheta+t a n^3thetacos e ctheta=(...

    Text Solution

    |

  16. If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasin...

    Text Solution

    |

  17. If 2t a n^2alphat a n^2betat a n^2gamma+t a n^2alphat a n^2beta+t a ...

    Text Solution

    |

  18. If m^2 + m'^2 + 2mm' costheta = 1 and n^2+n'^2+2n n'costheta=1, (mn +...

    Text Solution

    |

  19. If (sin^4theta)/a+(cos^4theta)/b=1/(a+b) , prove that (sin^8theta)/(a...

    Text Solution

    |

  20. If (cos^4alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 prove that (i...

    Text Solution

    |