Home
Class 11
MATHS
Prove that: |sintheta."sin"(60-theta).si...

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

Text Solution

AI Generated Solution

To prove that \( |\sin \theta \cdot \sin(60^\circ - \theta) \cdot \sin(60^\circ + \theta)| \leq \frac{1}{4} \) for all values of \( \theta \), we can follow these steps: ### Step 1: Rewrite the expression We start with the expression: \[ |\sin \theta \cdot \sin(60^\circ - \theta) \cdot \sin(60^\circ + \theta)| \] ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

Prove that: |costhetacos(60^0-theta)cos(60^0+theta)lt=1/4 for all values of thetadot

Prove that sin theta sin(60^(@)-theta) sin(60^(@)+theta)=1/4 sin3theta .

Prove that : sin^(4)theta-cos^(4)theta=2sin^(2)theta-1

Solve that equation : sintheta+sin3theta+sin5theta=0.

If sin^2 theta=1/4 , then the value of theta is

Prove that sin^(4)theta+2sin^(2)thetacos^(2)theta+cos^(4)theta=1

If A=cos^2theta+sin^4theta, prove that 3/4lt=Alt=1 for all values of thetadot

Solve: sin4theta=sintheta

Prove that: sin theta- 1/2 sin 2 theta+1/3 sin 3theta-…to oo = theta/2

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

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: cos5A=16cos^5A-20cos^3A+5cosA

    Text Solution

    |

  2. Prove that: sin18^0=(sqrt(5)-1)/4 .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Prove that : cos4x=1-8sin^2xcos^2x

    Text Solution

    |

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

    Text Solution

    |

  13. Prove that : (sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If tanx=3/4, pi < x < (3pi)/2 , find the values of sinx/2, cosx/2 and...

    Text Solution

    |

  18. Prove that : cos 20^0cos 40^0cos 60^0cos 80^0=1/(16)

    Text Solution

    |

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

    Text Solution

    |

  20. Show that: sin 50^0cos95^0=(sqrt(2)sin35^0-1)/(2sqrt(2))

    Text Solution

    |