Home
Class 12
MATHS
sintheta/(1-cottheta)+costheta/(1-tanthe...

`sintheta/(1-cottheta)+costheta/(1-tantheta)=` (a)`theta` (b)1 (c)`costheta-sintheta` (d)`costheta+sintheta`

A

0

B

1

C

`cos theta-sin theta`

D

`cos theta + sin theta`

Text Solution

Verified by Experts

The correct Answer is:
D
`(sin theta)/(1-cot theta)+(cos theta)/(1-tan theta)`
`=(sin theta)/(1-(cos theta)/(sin theta))+(cos theta)/(1-(sin theta)/(cos theta))`
`=(sin^(2)theta)/(sin theta - cos theta)+(cos^(2)theta)/(cos theta - sin theta)`
`=(sin^(2)theta-cos^(2)theta)/((sin theta - cos theta))=sin theta + cos theta`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|2 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

(1-costheta)/(1+costheta)=((1-costheta)/(sintheta))^2=(cosectheta-cottheta)^2

Evaluate costheta.costheta+sintheta.sintheta

If sintheta+costheta=x then sintheta-costheta=?

If tantheta=(a)/(b) ,then find the value of (costheta+sintheta)/(costheta-sintheta) .

Prove that- costheta.tantheta=sintheta

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

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

costheta[(costheta, sintheta),(-sintheta,costheta)]+sintheta[(sintheta,-costheta),(costheta,sintheta)] is equal to (A) [(0,0),(1,1)] (B) [(1,1),(0,0)] (C) [(0,1),(1,0)] (D) [(1,0),(0,1)]

CENGAGE-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  2. sintheta/(1-cottheta)+costheta/(1-tantheta)= (a)theta (b)1 (c)costh...

    Text Solution

    |

  3. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  4. The value of (tan^(2)20^(@)-sin^(2)20^(@))/(tan^(2)20^(@).sin^(2)20^(@...

    Text Solution

    |

  5. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

    Text Solution

    |

  6. In DeltaABC, if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cos...

    Text Solution

    |

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

    Text Solution

    |

  8. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

    Text Solution

    |

  9. If tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4) is equal...

    Text Solution

    |

  10. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is

    Text Solution

    |

  11. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

    Text Solution

    |

  12. If x,y,z be all positive acute angles then the least value of tanx(cot...

    Text Solution

    |

  13. Three circles each of radius 1, touch one another externally and they ...

    Text Solution

    |

  14. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

    Text Solution

    |

  15. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  16. Which of the following is true ?

    Text Solution

    |

  17. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  18. Which of the following is greatest ?

    Text Solution

    |

  19. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  20. Which of the following is not correct ?

    Text Solution

    |