Home
Class 11
MATHS
Prove that: sin((4pi)/9+7)cos(pi/9+7)-co...

Prove that: `sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt(3))/2`

Text Solution

Verified by Experts

Given as `sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)`
LHS
`sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)`
As we know that `sin(A - B) - sin A cos B - cos A sin B`
Therefore,
`sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)`
=`sin((4pi)/9+7-pi/9+7)`
=`sin(pi/3)`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7) .

Prove that cos((2pi)/7)cos((4pi)/7)cos((8pi)/7)=1/8

Prove that cos((2pi)/7) cos((4pi)/7) cos((8pi)/7) =1/8

Prove that 4cos(2 pi)/(7)*cos(pi)/(7)-1=2cos(2 pi)/(7)

Prove that: cos(pi)/(7)cos(2 pi)/(7)cos(4 pi)/(7)=-(1)/(8)

prove that cos2(pi)/(7)+cos4(pi)/(7)+cos6(pi)/(7)=-(1)/(2)

cos.(2pi)/(7)+cos.(4pi)/(7)+cos.(6pi)/(7)

Prove that: sinpi/7+sin(2pi)/(7) + sin(8pi)/7 + sin(9pi)/7=0

Show that: sin((2pi)/7)+ sin ((4pi)/7) + sin( (8pi)/7) = sqrt7/2 .

Prove that: sin((3pi)/(8)-5)cos((pi)/(8)+5)+cos((3pi)/(8)-5)sin((pi)/(8)+7)=1

RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. (cos9^@+sin9^@)/(cos9^@-sin9^@)= (a) tan 54^@ (b) tan 36^@ (d) None of...

    Text Solution

    |

  2. Prove that: sin(60^0-theta)-cos(30^0+theta)=0.

    Text Solution

    |

  3. Prove that: sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt...

    Text Solution

    |

  4. Prove that: sin((3"pi")/8-5)cos("pi"/8+5)+cos((3"pi")/8-5)sin("pi"/8+7...

    Text Solution

    |

  5. Prove that :(tan69^@+tan 66^@)/(1-tan 69^@tan66^@)=-1

    Text Solution

    |

  6. If tanA=5/6 and tanB=1/(11),\ p rov e\ t h a t\ A+B=pi/4

    Text Solution

    |

  7. If tanA=m/(m-1)\ and tanB=1/(2m-1), then prove that A-B=\ pi/4

    Text Solution

    |

  8. Prove that: cos^2 45^@-sin^2 15^@=(sqrt(3))/4

    Text Solution

    |

  9. Prove that: sin^2(n+1)A-sin^2n A="sin"(2n+1)A s in A

    Text Solution

    |

  10. Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=t a n A

    Text Solution

    |

  11. Prove that: (sin(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+(sin(C-A)...

    Text Solution

    |

  12. Prove that: ("sin"(A-B))/(s in A s in B)+("sin"(B-C))/(s in B s in C)+...

    Text Solution

    |

  13. Prove that: sin^2B=sin^2A+sin^2(A-B)-2sin A cos B sin(A-B)

    Text Solution

    |

  14. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

    Text Solution

    |

  15. Prove that: (tan(A+B))/(cot(A-B))=\ (tan^2A-tan^2B)/(1-tan^2Atan^2B)

    Text Solution

    |

  16. If tan A= xtanB then prove that sin(A-B)/sin(A+B)=(x-1)/(x+1)

    Text Solution

    |

  17. If tan(A+B)=x and tan(A-B)=y then find the values of tan2A and tan2B

    Text Solution

    |

  18. If cos A+sin B=m and sin A+cos B=n , prove that 2sin(A+B)=m^2+n^2-2.

    Text Solution

    |

  19. If tan A+tan B=a and cot A+cot B=b , prove that: cot(A+B)=1/a-1/b

    Text Solution

    |

  20. If sin(alpha+beta)=1 and sin(alpha-beta)=1/2, where 0lt=alpha, betalt=...

    Text Solution

    |