Home
Class 11
MATHS
Prove that: (costheta)/(1+sintheta)=tan(...

Prove that: `(costheta)/(1+sintheta)=tan(pi/4-theta/2)`

Text Solution

Verified by Experts

`L.H.S.=costheta/(1+sintheta ) `
`=sin(pi/2−theta)/(1+cos(pi/2−theta))`
Using `sin2x=2sinxcosx and 1+cos^2x=2cos2x `
`=[2sin(pi/4−theta/2)cos(pi/4−theta/2)]/(2cos^2(pi/4−theta/2)) `
`=(sin(pi/4−theta/2))/(cos(pi/4−theta/2)) `
`=tan(pi/4−theta/2)=R.H.S`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec "theta

Prove that sec theta + tan theta = tan (pi/4 + theta/2)

Prove that : (cos^(2)theta)/(1-tantheta)+(sin^(3)theta)/(sintheta-costheta)=1+sinthetacostheta

Prove the following Identities (1+sin theta-costheta)/(1+ sintheta+costheta)= tan(theta/2)

Show that (1+tan .theta/2)/(1-tan. theta/2)=(1+sintheta)/(cos theta)=tan(pi/4+theta/2)

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

Prove that: sqrt((1-sintheta)/(1+sintheta))= sec theta- tan theta when (-pi/2) < theta < pi/2 and -sec theta+tan theta when pi/2< theta< (3pi)/2

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

Prove that: sqrt((1-sintheta)/(1+sintheta))=sectheta -tan theta .

Prove that : tan((pi)/(4)+theta)+tan((pi)/(4)-theta)=2sec2 theta

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

    Text Solution

    |

  2. Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

    Text Solution

    |

  3. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

    Text Solution

    |

  4. Prove that: sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

    Text Solution

    |

  5. Prove that: (cosalpha+cosbeta)^2+(s inalpha+s inbeta)^2=4cos^2\ \ ((al...

    Text Solution

    |

  6. Prove that: 1+cos^2 2x=2(cos^4x+sin^4x)

    Text Solution

    |

  7. cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

    Text Solution

    |

  8. Prove that : (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

    Text Solution

    |

  9. Prove that:cos^2(pi/4-theta)-sin^2(pi/4-theta)=s in2theta

    Text Solution

    |

  10. Prove that: cos4A=1-8cos^2A+8cos^4 A

    Text Solution

    |

  11. Prove that 3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13

    Text Solution

    |

  12. cos^6A-sin^6A=cos2A(1-1/4sin^2 2A)

    Text Solution

    |

  13. Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta .

    Text Solution

    |

  14. Prove that: cot^2A-tan^2A=4 cot2A cosec2A

    Text Solution

    |

  15. sin4A=4sinAcos^3A-4cosAsin^3A

    Text Solution

    |

  16. Prove that: \ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2

    Text Solution

    |

  17. If cos x=\ -3/5a n d\ x lies in the IIIrd quadrant, find the values of...

    Text Solution

    |

  18. If cos x=-3/5a n d\ x lies in IIInd quadrant, find the values of sin2x...

    Text Solution

    |

  19. If sinx=(sqrt(5))/3a n d\ x lies in IInd quadrant, find the values of ...

    Text Solution

    |

  20. Prove that 1+cos^2 2x=2(cos^4x+sin^4x)

    Text Solution

    |