Home
Class 12
MATHS
Prove that tanpi/(16)+2tanpi/8+4=cotpi/(...

Prove that `tanpi/(16)+2tanpi/8+4=cotpi/(16)` .

A

`cot ""(pi)/(8)`

B

`cot""(pi)/(16)`

C

`cot""(pi)/(16)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We know that `tan theta =cot theta -2 cot 2theta`
`thereforetan""(pi)/(16)+2 tan""(pi)/(8)+4`
`(cot""(pi)/(16)-2cot""(pi)/(8))+2(cot""(pi)/(8)-2cot""(pi)/(4))+4=cot""(pi)/(16)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|189 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

Prove that tan(pi/16)+2tan(pi/8)+4=cot (pi/16) .

Prove that tan(pi/16)+2tan(pi/8)+4=cot(pi/6) .

Prove that tanpi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Prove that cos(2pi)/(15)cos(4pi)/(15)cos(8pi)/(15)cos(14pi)/(15)=1/(16)

Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15) = (1)/(16).

Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

The value of 2tanpi/(10)+3secpi/(10)-\ 4cospi/(10) is 0 b. 1 c. sqrt(5) d. none of these

Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15))=1/(16)

Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15))=1/(16)

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  2. The maximum value of (cos alpha(1))(cos alpha(2))... ( cos alpha(n)) u...

    Text Solution

    |

  3. Prove that tanpi/(16)+2tanpi/8+4=cotpi/(16) .

    Text Solution

    |

  4. If sin A=a cos B and cosA=b sinB then, (a^2 - 1) tan^2 A+(1 -b^2)ta...

    Text Solution

    |

  5. If (pi)/(2)lt thetalt(3pi)/(2),then sqrt((1-sintheta)/(1+sintheta))"is...

    Text Solution

    |

  6. If cos^(4)theta sec^(2)alpha, 1/2 and sin^(4)theta cosec^(2) alpha ar...

    Text Solution

    |

  7. If 4 n alpha= pi, then cot alpha cot 2alpha cot 3alpha...cot( 2n-1)alp...

    Text Solution

    |

  8. If sinx+sin^2x+sin^3x=1 then find the value of cos^6x-4cos^4x+8cos^2x

    Text Solution

    |

  9. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

    Text Solution

    |

  10. If A+B=pi/3" where "A, B gt 0, then minimum value of sec A + sec B is ...

    Text Solution

    |

  11. If cos(theta - alpha) , costheta , cos(theta + alpha) are in H.P. then...

    Text Solution

    |

  12. If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(4pi)/3) , prove that ...

    Text Solution

    |

  13. If 2 sin alpha cos beta sin gamma=sin beta sin( alpha-gamma). Then, s...

    Text Solution

    |

  14. If cos 5 theta = a cos^(5)theta + b cos^(3)theta+c cos theta. Then, fi...

    Text Solution

    |

  15. Given tan A and tan B are the roots of x^2-ax + b = 0, The value of si...

    Text Solution

    |

  16. The value of sin^(6)((pi)/(49))+cos^(6)((pi)/(49))-1+3sin^(2)((pi)/(...

    Text Solution

    |

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

    Text Solution

    |

  18. If sin2 theta=3/4, then sin^(3)theta+cos^(3)theta=

    Text Solution

    |

  19. Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to 4x ...

    Text Solution

    |

  20. If A+B=pi/3, and cosA+cosB=1, then which of the following is true:

    Text Solution

    |