Home
Class 11
MATHS
Prove that: (sin2theta)/(1+cos2theta+sin...

Prove that: `(sin2theta)/(1+cos2theta+sintheta)=t a ntheta`

Text Solution

Verified by Experts

`(frac{sin theta+sin 2 theta}{1+cos theta+cos 2 theta})`

`=(frac{sin theta+2 sin theta cos theta}{1+cos 2 theta+cos theta})`

`=(frac{sin theta(1+2 cos theta)}{1+2 cos ^{2} theta-1+cos theta})`

`=(frac{sin theta(1+2 cos theta)}{cos theta(1+2 cos theta)})=tan theta={RHS}`

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: (sin2 theta)/(1+cos2 theta)=tan theta

Prove that: (sin2 theta)/(1-cos2 theta)=cot theta

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that: (a) (sin 2 theta)/(1+cos 2 theta)=tan theta (b) (1+sin 2 theta+2theta)/(1+sin2 theta-cos 2 theta)=cot theta

Prove that : (sin^(2)theta)/(cos theta)+cos theta=sec theta

Prove that: a) (sin2theta)/(1+cos2theta) = tantheta b) (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cottheta

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

Prove that- 1-cos^2theta/(1+sintheta)=sintheta

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

Prove that: :(1+sin theta-cos theta)/(1+sin theta+cos theta)=tan(theta)/(2)

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: sin18^@=(sqrt(5)-1)/4 .

    Text Solution

    |

  2. Prove that: |sintheta"sin"(60-theta)sin(60+theta)|lt=1/4 for all value...

    Text Solution

    |

  3. Prove that: (sin2theta)/(1+cos2theta+sintheta)=t a ntheta

    Text Solution

    |

  4. Prove that sin(2theta)/(1-cos2theta)=cot theta

    Text Solution

    |

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

    Text Solution

    |

  6. Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

    Text Solution

    |

  10. cos4x=1-8sin^2xcos^2x

    Text Solution

    |

  11. Prove that: (sin5x-2sin3x+sin x)/(cos5x-cos x)=tanx

    Text Solution

    |

  12. (sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

    Text Solution

    |

  13. Express each of the following as the sum or difference of sines and ...

    Text Solution

    |

  14. Show that sqrt(3)\ cos e c\ 20^0-sec20^0=4.

    Text Solution

    |

  15. Prove that: tan4theta=(4t a ntheta(1-tan^2theta))/(1-6tan^2theta+tan^4...

    Text Solution

    |

  16. If tanx=3/4,pi<x<(3pi)/2 , fid the values of sinx/2,cosx/2a n dtanx//2...

    Text Solution

    |

  17. Find : cos 20^0cos 40^0cos 60^0cos 80^0

    Text Solution

    |

  18. Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

    Text Solution

    |

  19. Show that: sin 50^0cos85^0=(1-sqrt(2)sin35^0)/(2sqrt(2))

    Text Solution

    |

  20. Prove that cos(2pi/15)cos(4pi/15)cos(8pi/15)cos(14pi/15)=1/16

    Text Solution

    |