Home
Class 11
MATHS
Solve the following equation: costheta\ ...

Solve the following equation: `costheta\ cos2theta\ cos3theta=1/4`

Text Solution

Verified by Experts

`costhetacos2thetacos3theta=1/4`
⇒`1/2​(2cos3thetacostheta)cos2theta=1/4`
⇒`(cos4theta+cos2theta)cos2theta=1/2`
⇒`cos4thetacos2theta+cos^2 2theta=1/2`
⇒`cos4thetacos2theta+(1+cos4theta​)/2=1/2​`
⇒`cos4thetacos2theta+1/2cos4theta=0`
⇒`cos4theta(cos2theta+1/2​)=0`
`cos4theta=0, cos2theta=(−1)/2​`
...
Promotional Banner

Topper's Solved these Questions

  • TRANSFORMATION FORMULAE

    RD SHARMA|Exercise Solved Examples And Exercises|145 Videos

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

Similar Questions

Explore conceptually related problems

Solve the following equation: cos4 theta=cos2 theta

Solve the following equation: cos theta+cos2 theta+cos3 theta=0

Solve the following equation: cos theta+cos3 theta-cos2 theta=0

cos theta cos2 theta cos3 theta=(1)/(4)

Solve the following equation: sin3 theta+cos2 theta=0

Solve the following equation: sin2 theta+cos theta=0

Solve the following equation: cos^(2)theta-sin theta cos theta-(1)/(2)=0

Solve that following equations: sin theta+cos theta=1

costheta-cos2theta=sin3theta

RD SHARMA-TRIGONOMETRIC EQUATIONS-Solved Examples And Exercises
  1. Solve the following equation: sin3theta-sintheta=4cos^2theta-2

    Text Solution

    |

  2. Solve the following equation: costheta+cos3theta-cos2theta=0

    Text Solution

    |

  3. Solve the following equation: costheta\ cos2theta\ cos3theta=1/4

    Text Solution

    |

  4. Solve the following equation: sintheta+sin2theta+sin3theta+ sin4theta=...

    Text Solution

    |

  5. Solve the following equation: sin2theta-sin4theta+sin6theta=0

    Text Solution

    |

  6. Solve the following equation: tantheta+tan2theta+tan3theta=0

    Text Solution

    |

  7. Write the general solution of tan^2 2x=1.

    Text Solution

    |

  8. Solve the equation 5cos^2 theta+7sin^2theta-6=0

    Text Solution

    |

  9. Writhe the number of values of theta\ in\ [0,2pi] thast satisfy the eq...

    Text Solution

    |

  10. If 2sin^2theta=3\ costheta,\ w h e r e\ 0lt=thetalt=2pi, then find the...

    Text Solution

    |

  11. The smallest value of theta satisfying the equation sqrt(3)(cottheta+t...

    Text Solution

    |

  12. If costheta+sqrt(3)sintheta=2, then theta= a.pi//3 b. 2pi//3 c. 4pi//...

    Text Solution

    |

  13. The general solution of the equation 7cos^2theta+3sin^2theta=4 is thet...

    Text Solution

    |

  14. A solution of the equation cos^2theta+sintheta+1=0 lies in the interva...

    Text Solution

    |

  15. The number of solution in [0,pi//2] of the equation cos3xtan5x=sin7x i...

    Text Solution

    |

  16. The general value of x satisfying the equation satisfying the equati...

    Text Solution

    |

  17. The smallest positive angle which satisfies the equation 2sin^2theta+s...

    Text Solution

    |

  18. If 4sin^2theta=1, then the values of theta are 2npi+-pi/3,\ n in Z b....

    Text Solution

    |

  19. If cottheta-t a ntheta=s e ctheta , then theta is equal to 2npi+(3pi)/...

    Text Solution

    |

  20. A value of theta satisfying costheta+sqrt(3)sintheta=2 is (5pi)/3 b. (...

    Text Solution

    |