Home
Class 10
MATHS
Prove that tan20^(@)+tan70^(@)=(sec^(2)2...

Prove that `tan20^(@)+tan70^(@)=(sec^(2)20^(@))/(sqrt(sec^(2)20^(@)-1))`

Text Solution

Verified by Experts

`tan20^(@)+tan70^(@)`
`=tan20^(@)+tan(90^(@)-20^(@))`
`=tan20^(@)+cot20^(@)`
`=tan20^(@)+(1)/(tan20^(@))=(tan^(2)20^(@)+1)/(tan20^(@))`
`=(sec^(2)20^(@))/(sqrt(tan^(2)20^(@)))=(sec^(2)20^(@))/(sqrt(sec^(2)20^(@)-1))`
Hence `tan20^(@)+tan70^(@)=(sec^(2)20^(@))/(sqrt(sec^(2)20^(@)-1))`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|28 Videos

  • TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|66 Videos

  • VARIATION

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|59 Videos

Similar Questions

Explore conceptually related problems

Prove that tan20^(@) tan40^(@) tan80^(@) = sqrt3

Prove that tan70^(@)=2tan50^(@)+tan20^(@) .

Prove that tan20^@+4sin20^@=sqrt3

Prove that, tan 70^(@) = 2tan 50^(@) + tan 20^(@)

Show that tan 15^@+ tan 75^@ = (sec^2 15^@)/sqrt(sec^2 15^@-1)

Prove that : tan 70^(@)+ tan 10^(@)- tan 50^(@)= sqrt(3)

Show that : tan 20^(@)+ tan 70^(@)= 2 "cosec" 40^(@)

Prove that, tan 70^(@) - tan 50^(@) + tan 10^(@) = sqrt3

Prove that tan 70^@=tan 20^@+2tan50^@

int (sec^(2)xdx)/(sqrt(5sec^(2)x-12 tan x-1))

CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES -EXERCISE
  1. Prove that tan20^(@)+tan70^(@)=(sec^(2)20^(@))/(sqrt(sec^(2)20^(@)-1))

    Text Solution

    |

  2. If A, B, C are the angles of a triangle then tan ((B+C)/2)=

    Text Solution

    |

  3. (sin21^(@)30')/(cos68^(@)30')

    Text Solution

    |

  4. (sin52^(@)+cos38^(@))/(sin38^(@)+cos52^(@))

    Text Solution

    |

  5. If sec9theta=cosec9theta, then the value of theta is equal to

    Text Solution

    |

  6. If the sum of any two acute angles be 180^(@), then they are called cm...

    Text Solution

    |

  7. If sin(theta+36^(@))=costheta then the value of theta" is "27^(@)

    Text Solution

    |

  8. The complementary angle of 90^(@) is

    Text Solution

    |

  9. If in DeltaABC,angleC=90^(@) then 1+tan^(2)A

    Text Solution

    |

  10. If theta=0^(@) then the trigonometrical ratio tangent of complementary...

    Text Solution

    |

  11. Find the value of cos1^(@)cos2^(@)cos3^(@).............cos180^(@)

    Text Solution

    |

  12. If 0^(@)angletheta angle20^(@), then find the value of theta when sin^...

    Text Solution

    |

  13. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2), then then the value of (x...

    Text Solution

    |

  14. If X, Y, Z are the angles of a DeltaXYZ then prove that cos^(2)""(X)/...

    Text Solution

    |

  15. If x=acos(90^(@)-theta)andy=bcot(90^(@)-theta), then prove that (a^(2)...

    Text Solution

    |

  16. Prove that (1+sec22^(@)+cot68^(@))(1-cosec22^(@)+tan68^(@))=2

    Text Solution

    |

  17. If angleA+angleB=90^(@) then prove that 1+(cotA)/(cotB)=cosec^(2)A

    Text Solution

    |

  18. If alpha+beta=90^(@), then find the value of cotbeta+cosbeta-(cosbeta)...

    Text Solution

    |

  19. Find the value of (5sin75^(@)sin77^(@)+2cos13^(@)cos15^(@))/(cos15^(@)...

    Text Solution

    |

  20. If alpha+beta=90^(@) then prove that cosec^(2)alpha+cosec^(2)beta=cose...

    Text Solution

    |

  21. Prove that sec^(2)11^(@)-(1)/(tan^(2)79^(@))=1.

    Text Solution

    |