Home
Class 11
MATHS
Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2)...

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

Text Solution

Verified by Experts

Given,
`tan(pi)/(16)`
`=>(sin(pi)/16)/(cos(pi)/16)`
divinding by `(2sin(pi))/16` both sides,
`=>(2sin^2(pi)/16)/(2sin(pi)/16cos(pi)/16)`
`=>(1-cos^2(2pi)/(16))/(sin(2pi)/(16))`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

tan backslash(pi)/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Show that tan pi/16 = sqrt(4 +2 sqrt2) - (sqrt2+1) .

Prove that 2 "cos" pi/16=sqrt(2+sqrt(2+sqrt2))

Prove that ,tan7(1)/(2)@=(sqrt(4-sqrt(6)-sqrt(2)))/(sqrt(3)*sqrt(2)+sqrt(6)-4)

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2 cos^(-1)x , 0

Prove that : tan^(-1) [ (sqrt(1+z) +sqrt(1-z))/(sqrt(1+z) -sqrt(1-z))] = pi/4 +1/2 cos^(-1) z

Prove that: tan142(1^(@))/(2)=2+sqrt(2)-sqrt(3)-sqrt(6)

Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x+sqrt(1-x)))]=(pi)/(4)-(1)/(2)cos^(-1)x,quad -(1)/(sqrt(2))<=x<=1

Prove that: "tan" 142(1^(@))/(2)=2+sqrt2-sqrt3-sqrt6 .

Prove that: cot(pi)/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that cos^3A+cos^3(120^0+A)+cos^3(240^0+A)=3/4cos3A

    Text Solution

    |

  2. Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

    Text Solution

    |

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

    Text Solution

    |

  4. Prove that tan7 1^circ/2 = sqrt6 - sqrt3 + sqrt2 - 2.

    Text Solution

    |

  5. Prove that:(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Text Solution

    |

  6. Prove that: (cosA+cosB)^2+(sinA-sinB)^2=4cos^2((A+B)/2) .

    Text Solution

    |

  7. Prove that: (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)=1/8

    Text Solution

    |

  8. If sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

    Text Solution

    |

  9. Find the value of sin(pi/10) sin((13pi)/10)

    Text Solution

    |

  10. Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0<theta<pi 8<=...

    Text Solution

    |

  11. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

    Text Solution

    |

  12. If tan(pi/4+theta/2)=tan^3(pi/4+alpha/2) then sin(theta)=(sin(alpha)(...

    Text Solution

    |

  13. If sin(theta+alpha)=aa n dsin(theta+beta)=b , prove that cos2(alpha-be...

    Text Solution

    |

  14. Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

    Text Solution

    |

  15. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove...

    Text Solution

    |

  16. If costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(th...

    Text Solution

    |

  17. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

    Text Solution

    |

  18. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1) (2cos2thet...

    Text Solution

    |

  19. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

    Text Solution

    |

  20. Prove that: sin3e sin^3e+cos3ecos^3e=cos^3 2e

    Text Solution

    |