Home
Class 11
MATHS
Prove that: cos18^0=(sqrt(10+2sqrt(5)))/...

Prove that: `cos18^0=(sqrt(10+2sqrt(5)))/4` .

Text Solution

AI Generated Solution

To prove that \( \cos 18^\circ = \frac{\sqrt{10 + 2\sqrt{5}}}{4} \), we will follow these steps: ### Step 1: Establish the relationship using sine We know that: \[ \cos^2 \theta + \sin^2 \theta = 1 \] Let \( \theta = 18^\circ \). Therefore, ...
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

Prove that: sin36^(0)=(sqrt(10-2sqrt(5)))/(4)

Prove that : sin 75^0 = (sqrt(6) + sqrt(2))/4

Prove that: sin18^(0)=(sqrt(5)-1)/(4)

Prove that: cos36^(@)=(sqrt(5)+1)/(4)

Statement -1: If xin[-1//sqrt(3),1//sqrt(3)] then cot^(-1)((3x-x^(3))/(1-3x^(2)))=cos^(-1)((1-x^(2))/(1+x^(2)))rarrx=sqrt(25-10sqrt(5))/(5) statement -2: sin18^(@)=sqrt(5-1)/(4) and cos18^(@)=sqrt(10+2sqrt(5))/4

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that: sqrt(2+sqrt(2+sqrt(2+2cos8A)))=2cosA

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

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. What is the value of cos36^@ .

    Text Solution

    |

  2. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

    Text Solution

    |

  3. Prove that: cos18^0=(sqrt(10+2sqrt(5)))/4 .

    Text Solution

    |

  4. If t a ntheta/2=sqrt((1-e)/(1+e))tan(alpha/2), then cosalpha= (a) 1-...

    Text Solution

    |

  5. If cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2x is equal to

    Text Solution

    |

  6. If alphaa n dbeta are acute angles satisfying cos2alpha=(3cos2beta-1)/...

    Text Solution

    |

  7. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

    Text Solution

    |

  8. Prove that: cos^(2)48^(@)-sin^(2)12^(@)=(sqrt(5)+1)/(8)

    Text Solution

    |

  9. The value of (sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha) is

    Text Solution

    |

  10. If costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)),t h e nlambda= ...

    Text Solution

    |

  11. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

    Text Solution

    |

  12. If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

    Text Solution

    |

  15. Prove that: cos^2 48^0-sin^2 12^0=(sqrt(5)+1)/8

    Text Solution

    |

  16. Find sin x/2 ,cos x/2 and tan x/2 of the following : tanx=-4/3,""x in...

    Text Solution

    |

  17. Find the values of cospi/8

    Text Solution

    |

  18. Prove that: sin(pi/14)sin((3pi)/14)sin((5pi)/14)sin((7pi)/14)sin((9pi...

    Text Solution

    |

  19. Prove that: (1+sec2theta)(1+sec4theta)(1+sec8theta)(1+sec2^ntheta)=t a...

    Text Solution

    |

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

    Text Solution

    |