Home
Class 11
MATHS
Prove that: sin3e sin^3e+cos3ecos^3e=cos...

Prove that: `sin3e sin^3e+cos3ecos^3e=cos^3 2e`

Text Solution

Verified by Experts

Given,
`sin3e sin^3e+cos3ecos^3e=cos^3 2e`
we know that,
`cos3e=4cos^3e-3cose`
`sin3e=3sine-4sin^3e`
so,
L.H.S
=`sin3e sin^3e+cos3ecos^3e`
...
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: (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

Prove that (sin5A-sin3A)/(cos5A+cos3A)=tan A

prove that (sin A-2sin^(3)A)/(2cos^(3)A-cos A)=tan A

Prove that : cos^(3)A cos3A+sin^(3)A sin3A=cos^(3)2A

Prove that: (sin5A-sin3A)/(cos5A+cos3A)=tan A(sin A+sin3A)/(cos A+cos3A)=tan2A

Prove that (sin5A- sin3A)/(cos 5A +cos 3A)= tanA

e^(3x)cos 2x

Prove that (sin A+cos A)(1-sin A cos A)=sin^(3)A+cos^(3)A

Prove that sin A+sin2A+sin4A+sin5A=4((cos A)/(2))(cos3(A)/(2))sin3A

Prove that cos ^ (3) and cos3e + sin ^ (3) and sin3e = cos ^ (3) 2e

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1) (2cos2thet...

    Text Solution

    |

  2. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

    Text Solution

    |

  3. Prove that: sin3e sin^3e+cos3ecos^3e=cos^3 2e

    Text Solution

    |

  4. If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+co...

    Text Solution

    |

  5. If costheta=(cosalpha-cosbeta)/(1-sinalphasinbeta) , prove that one v...

    Text Solution

    |

  6. If costheta=(cosalpha-cosbeta)/(1-cosalpha.cosbeta) , prove that t a n...

    Text Solution

    |

  7. sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A

    Text Solution

    |

  8. Prove that: cos5A=16cos^5A-20cos^3A+5cosA

    Text Solution

    |

  9. Prove that: sin18^@=(sqrt(5)-1)/4 .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |