Home
Class 11
MATHS
Prove the following identity: cos^3theta...

Prove the following identity: `cos^3thetasin3theta+sin^3thetacos3theta=3/4sin4thetadot`

Text Solution

AI Generated Solution

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 the following identities: (sin^3theta+cos^3theta)/(sintheta+costheta)+sinthetacostheta=1

Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 theta .

Prove the following identity: ((1+cottheta+t a ntheta)(sintheta-costheta))/(sec^3theta-cos e c^3theta)=sin^2thetacos^2theta

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

Solve 4sintheta sin2thetasin4theta=sin3theta

Prove the following identities: sin^8theta-cos^8theta=(sin^2theta-cos^2theta)(1-2sin^2thetacos^2theta)

Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0 sin^6theta+cos^6theta+3sin^2thetacos^2theta=1 (sin^8theta-cos^8theta)=(sin^2theta-cos^2theta)(1-2s in^2thetacos^2theta)

Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=(1-2sin^2thetacos^2theta)/(sintheta\ costheta)

Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)

Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. prove sin(5theta) = 16sin^5(theta)-20sin^3(theta)+5sin(theta)

    Text Solution

    |

  2. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

    Text Solution

    |

  3. Prove the following identity: cos^3thetasin3theta+sin^3thetacos3theta=...

    Text Solution

    |

  4. Prove the following identity: \ t a nthetat a n(theta+60^0)+t a ntheta...

    Text Solution

    |

  5. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

    Text Solution

    |

  6. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

    Text Solution

    |

  7. Prove the following identity: cot A+cot(60^0+A)+cot(120^0+A)=3cot3A

    Text Solution

    |

  8. Prove that: sin^3A+sin^3((2pi)/3+A)+sin^3((4pi)/3+A)=-3/4sin3Adot

    Text Solution

    |

  9. Prove that: |costhetacos(60^0-theta)cos(60^0+theta)lt=1/4 for all valu...

    Text Solution

    |

  10. Prove that: sin(pi/5) sin2pi/5 sin3pi/5 sin4pi/5=5/16

    Text Solution

    |

  11. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15...

    Text Solution

    |

  12. Prove that: sin 12^0sin 48^0sin 54^0=1/8dot

    Text Solution

    |

  13. The value oif the expressin (1+cospi/10)(1+cos(3pi)/10)(1+cos(7pi)/10)...

    Text Solution

    |

  14. Prove that ; 4 sin 27^@=(5+sqrt(5))-sqrt((3-sqrt(5))) we have

    Text Solution

    |

  15. Prove that : sin^2(72^@) - sin^2 (60^@) = (sqrt5 - 1)/8

    Text Solution

    |

  16. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

    Text Solution

    |

  17. Prove that: sin^2 42^0-cos^2 78^0=(sqrt(5)+1)/8

    Text Solution

    |

  18. Prove that: cos 78^0cos 42^0cos 36^0=1/8

    Text Solution

    |

  19. Show that cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/1...

    Text Solution

    |

  20. Prove that cos6^@ . cos42^@. cos66^@ cos78^@= 1/16

    Text Solution

    |