Home
Class 11
MATHS
If tan x, tan y, tan z are in G.P., show...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise EXERCISE 5 (D) |60 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 cos x = cos y. cos 2z

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

If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/(y) , (x+y)/(z) are in A.P.

If the sum of all value of x satisfying the system of equations tan x + tan y+ tan x* tan y=5 sin (x +y)=4 cos x * cos y is (k pi )/2 , where x in (0, (pi)/(2)) then find the values of k .

If x,y,z are in G.P and a^x=b^y=c^z ,then

If x = a sec A cos B, y = b sec A sin B and z = c tan A, show that : (x^(2))/ (a^(2)) + (y^(2))/ (b^(2)) - (z^(2))/(c^(2)) = 1

ICSE-COMPOUND AND MULTIPLE ANGLES -CHEPTER TEST
  1. Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that ...

    Text Solution

    |

  2. Show that ( cos 10^(@) + sin 10 ^(@))/( cos 10^(@) - sin 10 ^(@)) = ta...

    Text Solution

    |

  3. If sin 2 A = 4/5, find the value of tan A, (0^(@) le A le (pi)/(3))

    Text Solution

    |

  4. Express cot A in terms of cos 2 A

    Text Solution

    |

  5. Write cos 4 theta in terms of cos theta.

    Text Solution

    |

  6. A positive acute angle is divided into two parts whose tangents are 1/...

    Text Solution

    |

  7. Show that cos 10^(@) + cos 110^(@) + cos 130^(@) = 0

    Text Solution

    |

  8. Show that (sin 5 A + 2 sin 8A + sin 11 A)/( sin 8A + 2 sin 11 A + sin ...

    Text Solution

    |

  9. Show that (1)/(2 sin 10^(@)) - 2 sin 70^(@) =1.

    Text Solution

    |

  10. Show that sin 19^(@) + sin 41^(@) + sin 83^(@) = sin 23 ^(@) + sin 37^...

    Text Solution

    |

  11. If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5) find the value of tan...

    Text Solution

    |

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

    Text Solution

    |

  13. If tan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the eq...

    Text Solution

    |

  14. Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B ...

    Text Solution

    |

  15. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

    Text Solution

    |

  16. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

    Text Solution

    |

  17. Prove that cos 6x = 32 cos ^(6) x - 48 cos ^(4) x + 18 cos ^(2) x -1.

    Text Solution

    |

  18. Prove that sin ^(2) 72 ^(@)- sin ^(2) 60 ^(@)= (sqrt5-1)/(8).

    Text Solution

    |

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

    Text Solution

    |

  20. If tan (alpha )/(2) : tan ""(beta)/(2) = 1 : sqrt3 show that cos beta...

    Text Solution

    |