Home
Class 11
MATHS
Prove that: Sin 4A = 4 cos^3 A sin A - ...

Prove that: ` Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A`

Text Solution

AI Generated Solution

To prove that \( \sin 4A = 4 \cos^3 A \sin A - 4 \sin^3 A \cos A \), we will start from the left-hand side and use trigonometric identities. ### Step 1: Start with the left-hand side We begin with the expression for \( \sin 4A \): \[ \sin 4A \] ...
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 sin4A=4sinAcos^3A-4sin^3A

Prove that : 2 sin^(2) A + cos^(4) A = 1 + sin^(4) A

Prove that: sin 3x + sin 2x - sin x = 4 sin x cos x/2 cos (3x)/2

If 4 cos^(2) A - 3 = 0 and 0^(@) le A le 90^(@), then prove that : sin 3 A = 3 sin A - 4 sin^(3) A

Show that sin 3 A + sin 2A -sin A = 4 sin A cos (A)/(2) cos "" (3A)/( 2)

Prove that : (1+sin 2A)/(cos 2A) = (cos A + sin A)/(cos A - sin A) = tan (pi/4 + A)

Prove that: (sin3A cos4A-sin Acos2A)/(sin4A sin A+cos6A cos A)=tan2A

Prove that a cos A + b cos B + c cos C = 4 R sin A sin B sin C.

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

Prove that: \ sin3A+sin2A-sin A=4sin A cos (A/2)cos((3A)/2)

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. If alpha and beta are distinct roots of acostheta+b sintheta=c , prove...

    Text Solution

    |

  2. Prove that: sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

    Text Solution

    |

  3. Prove that: Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A

    Text Solution

    |

  4. If tanA=1/7a n d tanB=1/3 , show that cos2A=sin4Bdot

    Text Solution

    |

  5. If 2t a nalpha/2=tan(beta/2) , prove that cosalpha=(3+5cosbeta)/(5+3c...

    Text Solution

    |

  6. If acos2theta+bsin2theta= c, alpha and beta as its roots , then prove ...

    Text Solution

    |

  7. If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+co...

    Text Solution

    |

  8. Prove that: 15sin(5pi)/(12)+15cos(5pi)/(12)-20sin^3(5pi)/(12)-20cos(5p...

    Text Solution

    |

  9. Prove that: sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)

    Text Solution

    |

  10. Find general solution of the trigonometric equation sin5theta =1

    Text Solution

    |

  11. Prove that: sin^4(pi/8)+sin^4((3pi)/8)+sin^4((5pi)/8)+sin^4((7pi)/8)=...

    Text Solution

    |

  12. Prove that: cos^4pi/8+cos^4(3pi)/8+cos^4(5pi)/8+cos^4(7pi)/8=3/2

    Text Solution

    |

  13. Prove that:tan6^0tan42^0tan66^0tan78^0=1.

    Text Solution

    |

  14. If tanalpha=(1-cosbeta)/(sinbeta),t h e n (a)tan3alpha=tan2beta (b) ...

    Text Solution

    |

  15. Prove that: sin36^0=(sqrt(10-2sqrt(5)))/4 .

    Text Solution

    |

  16. The value of (cos3theta)/(2cos2theta-1) is equal to (a) costheta (b) ...

    Text Solution

    |

  17. The value of cos^4theta+sin^4theta-6cos^2theta is (a) cos2theta (b) s...

    Text Solution

    |

  18. Prove that: sin(pi/10)+sin((13pi)/10)=-1/2

    Text Solution

    |

  19. If tan(pi//4+theta)+""tan(pi//4-theta)=lambdasec2theta,t h e nlambda= ...

    Text Solution

    |

  20. Prove that: (1+cos4x)/(cot x-tanx)=1/2sin4x

    Text Solution

    |