Home
Class 11
MATHS
If m tan (theta - 30^(@))= n tan (theta ...

If `m tan (theta - 30^(@))= n tan (theta + 120^(@)),` show that `cos 2 theta = (m +n)/(2 (m -n)).`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise EXERCISE 5 (C ) |30 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Chapter Test|25 Videos

  • CONIC SECTIONS

    ICSE|Exercise Multiple Choice Questions |33 Videos

Similar Questions

Explore conceptually related problems

If tan theta + tan (60^@+ theta) + tan (120^@ + theta)=3 then theta =

tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 cot 8 theta = cot theta.

If sin theta = n sin ( theta + 2 alpha ) , show that ( n -1) tan (theta + alpha ) + (n + 1) tan alpha = 0 .

If tan(alpha+theta)=ntan(alpha-theta) , show that (n+1)sin2theta=(n-1)sin2alphadot

If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta) , then show that theta = (pi)/(4) , when n is an y integer.

If sec theta + tan theta = m, show that ((m^(2) -1))/((m^(2) +1)) = sin theta .

If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha - theta) the prove that 2 theta = alpha - [ tan^(-1) ((n-m)/(n+m)) tan alpha]

If cos ec theta - sin theta = m and sec theta - cos theta = n, then show that (m ^(2) n ) ^(2//3) + (mn ^(2)) ^( 2//3) = 1.

A general solution of tan^(2) theta+ cos 2 theta=1 is (n in Z)

If tan^(4)theta +tan^(2) theta = 2 , then the value of cos^(4)theta +cos^(2)theta is-

ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. cos ^(2) 36^(@) + sin ^(2) 18^(@) = (3)/(4).

    Text Solution

    |

  2. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

    Text Solution

    |

  3. cos ^(2) 48^(@) - sin ^(2) 12 ^(@) = (sqrt5+1)/(8).

    Text Solution

    |

  4. Prove that sin "" (1)/(10) pi cos ""(1)/(5) pi = (1)/(4).

    Text Solution

    |

  5. sec 72 ^(@) - sec 36^(@) = 2.

    Text Solution

    |

  6. sin ^(2) 24 ^(@) - sin ^(2) 6^(@) = (sqrt5 -1)/(8).

    Text Solution

    |

  7. sin 12 ^(@) sin 48^(@) sin 54 ^(@) = (1)/(8).

    Text Solution

    |

  8. Prove that 4 cos 6^(@) cos 42 ^(@) cos 66^(@) cos 78^(@) = (1)/(4).

    Text Solution

    |

  9. sin "" (pi)/(5) sin "" (2pi)/(5) sin ""(4pi)/(5) sin""(3pi)/(5) = (5)/...

    Text Solution

    |

  10. Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "...

    Text Solution

    |

  11. cos ^(2) ""(pi)/(10) + cos ^(2) ""(2pi)/(5) + cos^(2) ""(3pi)/(5) + co...

    Text Solution

    |

  12. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

    Text Solution

    |

  13. cos alpha cos 2 alpha cos 4 alpha cos 8 alpha = (1)/(16), if alpha =...

    Text Solution

    |

  14. cos 12 ^(@) cos 24 ^(@) cos 36 ^(@) cos 48^(@) cos 72^(@) cos 84^(@) =...

    Text Solution

    |

  15. If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta c...

    Text Solution

    |

  16. If tan "" (x-y)/( 2 ), tan z, tan "" (x + y)/( 2) are in G.P. then sho...

    Text Solution

    |

  17. If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 th...

    Text Solution

    |

  18. If m tan (theta - 30^(@))= n tan (theta + 120^(@)), show that cos 2 th...

    Text Solution

    |

  19. If sin alpha = lamda sin (theta - alpha ) then prove that tan (alpha...

    Text Solution

    |

  20. If tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prov...

    Text Solution

    |