Home
Class 11
MATHS
If tan "" (x-y)/( 2 ), tan z, tan "" (x ...

If `tan "" (x-y)/( 2 ), tan z, tan "" (x + y)/( 2)` are in G.P. then show that `cos x = cos y. cos 2z`

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"(x-y)/(2)," tan z, tan"(x+y)/(2) are in G.P., then show that cosx=cosy*cos2z .

If "tan"(x-y)/(2),tanz,"tan"(x+y)/(2) are in G.P., then show that cosx=cosy*cos2z .

If tan x, tan y, tan z are in G.P., show that cos 2y = (cos (x +z))/(cos (x-z)).

If cosx + cosy + cosz = 0 and sinx + siny + sinz =0 , then show that cos (x-y) + cos(y - z) + cos(z - x) = - 3/2.

If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are also in A.P. then show that x=y=z and y≠0

If y = ( tan x)/( 1+ tan^2 x), Prove that (dy)/(dx) = cos 2x.

If tan x =(2b)/ (a- c) , y = acos^2 x + 2bsin x cos x + csin^2 x , z=asin^2 x-2b sin x cos x + c cos^2 x , prove that y-z=a-c .

If tan^(-1) x + tan^(-1)y + tan^(-1)z= pi then x + y + z is equal to

If 5 sin x cos y = 1, 4 tan x = tan y, then

If x+y=pi//4 and tan x+tan y=1 , then (n in Z)

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

    |