Home
Class 11
MATHS
Prove that (cos10^0+sin10^0)/(cos10^0-...

Prove that `(cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0`

Text Solution

Verified by Experts

`L.H.S. = (cos10^@ + sin10^@)/(cos10^@ - sin10^@)`
`=(cos10^@(1+tan10^@))/(cos10^@(1-tan10^@))`
`=(1+tan10^@)/(1-tan10^@)`
`=(tan45^@+tan10^@)/(1-tan45^@tan10^@)`
`=tan(45^@+10^@)`
`=tan55^@ = R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Prove that (cos10^(@)-sin10^(@))/(cos10^(@)+sin10^(@))=tan35^(@)

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

Prove that cos65^0+cos115^0=0

Prove the following identities: (cos10^(@)-sin10^(@))/(cos10^(@) + sin10^(@))=tan 35^(@)

Prove that cos20^0cos40^0cos60^0cos80^0=1/(16)dot

Show that 4(cos^3 10^@+sin^3 20^@)=3(cos10^@+sin20^@)

The value of (cos 10^(@) + sin 10^(@))/(cos 10^(@) -sin 10^(@))is-

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

Prove that cos36^0cos72^0cos108^0cos144^0=1/(16)dot

Prove that sin 20^(@) + sin 140^(@)-cos 10 ^(@) =0

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the range of f(x)=sin^2x-3sinx+2

    Text Solution

    |

  2. In a triangle DeltaXYZ, let a,b and c be the lengths of the sides opp...

    Text Solution

    |

  3. Prove that (cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0

    Text Solution

    |

  4. Find the range of f(x)=1/(4cosx-3)dot

    Text Solution

    |

  5. Find the general solutions of: 2^(1 + abscosx + abs(cosx)^2 + abs(co...

    Text Solution

    |

  6. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  7. If in triangle A B C ,/C=45^0 then find the range of the values of sin...

    Text Solution

    |

  8. Solve sqrt(3)costheta+sintheta=sqrt(2)

    Text Solution

    |

  9. Find the range of f(x)=1/(5sinx-6)

    Text Solution

    |

  10. Two parallel chords of a circle of radius 2 are at a distance. sqrt3+1...

    Text Solution

    |

  11. Prove that: sum(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

    Text Solution

    |

  12. The expression 3{sin^4((3pi/2)-alpha)+sin^4(3pi-alpha)} -2{sin^6(pi/2+...

    Text Solution

    |

  13. Solve sqrt(3)costheta-3sintheta=4sin2thetacos3thetadot

    Text Solution

    |

  14. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

    Text Solution

    |

  15. If alpha,beta,gamma, in (0,pi/2) , then prove that (sin(alpha+beta+gam...

    Text Solution

    |

  16. Find the number of integral value of n so that sinx(sinx+cosx)=n has a...

    Text Solution

    |

  17. In triangle ABC,angleC=(2pi)/3 and CD is the internal angle bisector ...

    Text Solution

    |

  18. Let P = [theta : sintheta – costheta = sqrt2 costheta) andQ= {theta : ...

    Text Solution

    |

  19. C(10,2) = C(n,2).Find n.

    Text Solution

    |

  20. Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...

    Text Solution

    |