Home
Class 11
MATHS
tan((11pi)/3)-2sin((9pi)/3)-3/4cosec^2(p...

`tan((11pi)/3)-2sin((9pi)/3)-3/4cosec^2(pi/4)+4cos^2((17pi)/6)=(3-2sqrt(3))/2`

Text Solution

Verified by Experts

Consider LHS
`=tan((11pi)/3)-2sin((9pi)/3)-3/4cosec^2(pi/4)+4cos^2((17pi)/6)`
`=tan 660^0 -2 sin120^0 - 3/4(cosec 45^0)^2 + 4(cos510^0)^2 `
`= tan (90^0 × 7 + 30^0) – 2 sin (90^0 × 1 + 30^0) – 3/4 [cosec 45^0]2 + 4 [cos (90^0 × 5 + 60^0)]2` ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Prove that: (a) cos510^(@) sin510^(@) + sin(-330^(@)) cos(-390^(@))=0 b) tan(11pi)/(3) -2sin(9pi)/3-3/4"cosec"^(2)pi/4 + 4cos^(2)(17pi)/6=(3-2sqrt(3))/2

2sin^(2)(pi/6)+cosec((7 pi)/6)cos^(2)(pi/3)=?

tan ((11 pi) / (3)) - 2sin ((9 pi) / (3)) - (3) / (4) cos ec ^ (2) ((pi) / (4)) + 4cos ^ ( 2) ((17 pi) / (6)) = (3-2sqrt (3)) / (2)

2(sin^(2)(pi/6)) +"cosec"(7pi)/(6)cos^(2)pi/3=3/2

(tan) (11 pi) / (3) (- 2sin) (4 pi) / (6) - (3) / (4) (cos ec ^ (2)) (pi) / (4) + (4cos ^ (2)) (17 pi) / (6) = (3-4sqrt (3)) / (2)

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

cos(pi/12)+sin^2((3pi)/12)+sin^2((9pi)/12)+cos((11pi)/12)=...

(sec^(2)(pi)/(4)-cot^(2)(pi)/(4))/(sin^(2)(pi)/(3)+cos^(2)(pi)/(6))+(sin^(2)(pi)/(2)-cos^(2)(pi)/(3))/((1)/(4)tan^(2)(pi)/(6))=9(2)/(3)

Prove that: (a) 2sin^(2)(pi/2) + "cosec"^(2)((7pi)/2) cos^(2)(pi/3)=(3/2)^2 (b) 2sin^(2)((3pi)/4)+2cos^(2)(pi/4)+2sec^(2)(pi/3)=10

2sin^(2)(3pi)/(4) + 2cos^(2)pi/4+2sec^(2)pi/3=10

RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Prove that: tan(-225^0)cot(-405^0)-tan(-765^0)cot(675^0)=0

    Text Solution

    |

  2. Prove that:cos 570^0sin510^0+sin(-330^0)cos(-390^0)=0

    Text Solution

    |

  3. tan((11pi)/3)-2sin((9pi)/3)-3/4cosec^2(pi/4)+4cos^2((17pi)/6)=(3-2sqrt...

    Text Solution

    |

  4. Prove that: 3sin(pi/6)sec(pi/3)-4sin((5pi)/6)cot(pi/4)=1

    Text Solution

    |

  5. In a DeltaA B C prove that cos(A+B)+cos C=0.

    Text Solution

    |

  6. In a Delta(ABC) prove that cos(("A"+"B")/2)=sin"C"/2dot

    Text Solution

    |

  7. In a "DeltaA B C prove that tan(("A"+"B")/2)=cot("C"/2)

    Text Solution

    |

  8. If A ,\ B ,\ C ,\ D be the angles of a cyclic quadrilateral, taken in ...

    Text Solution

    |

  9. Find x from the following equation: cos e c(90^@+theta)+x costhetacot(...

    Text Solution

    |

  10. Find x from the following equation: xcot(90^0+theta)+tan(90^0+theta)si...

    Text Solution

    |

  11. Prove that: t a n 720^0-cos 270^0-s in 150^0cos 120^0=1/4

    Text Solution

    |

  12. Prove that: sin 780^0sin 480^0+cos 120^0sin 150^0=1/2

    Text Solution

    |

  13. Prove that: sin780^0sin 120^0+cos 240^0sin390^0=1/2

    Text Solution

    |

  14. Prove that: sin600^0cos 390^0+cos 480^0sin 150^0=-1

    Text Solution

    |

  15. tan 225^@ cot 405^@+ tan 765^@ cot 675^@=0

    Text Solution

    |

  16. Write the maximum and minimum values of cos(cosx)

    Text Solution

    |

  17. Write the maximum and minimum values of s in\ (s in x)dot

    Text Solution

    |

  18. Write the maximum value of sin(cosx)dot

    Text Solution

    |

  19. If sin x=cos^2x ,\ then write the value of cos^2x\ (1+cos^2x)dot

    Text Solution

    |

  20. If sin x+cosec\ x=2, then write the value of sin^n x+cos e c^n xdot

    Text Solution

    |