Home
Class 11
MATHS
Prove that: cos^4pi/8+cos^4(3pi)/8+cos^4...

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

Text Solution

AI Generated Solution

To prove that \[ \cos^4\left(\frac{\pi}{8}\right) + \cos^4\left(\frac{3\pi}{8}\right) + \cos^4\left(\frac{5\pi}{8}\right) + \cos^4\left(\frac{7\pi}{8}\right) = \frac{3}{2}, \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8)=

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

cos^2(pi/8) +cos^2((3pi)/8) +cos^2((5pi)/8)+cos^2 ((7pi)/8)=2

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

Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

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

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

Statement I : sin^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8+sin^2(7pi)/8=2 Statement II sin^4pi/8+sin^4 (3pi)/8+sin^4(5pi)/8sin^4(7pi)/8=3/2

Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

Prove that "cos"(pi)/9."cos"(2pi)/9."cos"(3pi)/9."cos"(4pi)/9=1/(2^(4))

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan((alpha...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If pi < x < 2pi, prove that (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+...

    Text Solution

    |

  5. If f(x)=2(7cosx+24sinx)(7sinx-24cosx), for every x in R , then maximu...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that sqrt(sin^4x+4cos^2x)-sqrt(cos^4x+4sin^2x)=cos2xdot

    Text Solution

    |

  8. If cos^2A+cos^2B+cos^2C=1, t h e n ABC is (a)equilateral (b) isoscele...

    Text Solution

    |

  9. Number of triangles A B C if tanA=x ,tanB=x+1,a n dtanC=1-x is

    Text Solution

    |

  10. Which of the following quantities are rational? (a)sin((11pi)/(12))sin...

    Text Solution

    |

  11. If log(10)sin x + log(10)cos x=-1 and log(10)(sin x + cos x)=((log(10)...

    Text Solution

    |

  12. If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a)tanalpha=2tanbet...

    Text Solution

    |

  13. If cosbeta is the geometric mean between sinalphaa n dcosalpha, wher...

    Text Solution

    |

  14. In a triangle A B C , if A-B=120^0a n dsin(A/2)sin(B/2)sin(C/2)=1/(32...

    Text Solution

    |

  15. In a triangle PQR, ∠R=π/2.If tan(P/2) & tan(Q/2), are the roots of the...

    Text Solution

    |

  16. If (tanx)/2=(tany)/3=(tanz)/5,x+y+z=pi and tan^2x+tan^2y+tan^2z is

    Text Solution

    |

  17. In A B C , if sin^3theta=sin(A-theta)sin(B-theta)sin(C-theta) , then ...

    Text Solution

    |

  18. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

    Text Solution

    |

  19. Find the sum of the series cos e ctheta+cos e c2theta+cos e c4theta+ t...

    Text Solution

    |

  20. If tan6theta=p/q , find the value of 1/2(pcosec2theta-qsec2theta)

    Text Solution

    |