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

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MODEL TEST PAPER - 10

    ICSE|Exercise SECTION - B (In sub-parts (i) and (ii) choose the correct option and in sub - parts (iii) to (v), answer the questions as instructed.)|5 Videos

  • MODEL TEST PAPER - 10

    ICSE|Exercise SECTION - B |5 Videos

  • MODEL TEST PAPER - 10

    ICSE|Exercise SECTION - C |5 Videos

  • MODEL TEST PAPER - 18

    ICSE|Exercise SECTION - C|9 Videos

  • MODEL TEST PAPER - 17

    ICSE|Exercise SECTION -C|10 Videos

Similar Questions

Explore conceptually related problems

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

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

If 1/6 sinx, cosx, tan x are in G.P. then x=,

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

In DeltaABC , If x= tan((B-C)/2) tan(A/2),y= tan((C-A)/2)tan(B/2), z=tan((A-B)/2) tan(C/2) , then x+y+z (in terms of x, y, z only) is

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

If x,y,z are in AP and tan^(-1)x,tan^(-1)y,tan^(-1)z are also in AP, then

Show that (sinx-siny)/(cosx+cosy)=tan((x-y)/2)

ICSE-MODEL TEST PAPER - 10 -SECTION - A
  1. Find the domain and range of f(x)=(x+2)/(|x+2|).

    Text Solution

    |

  2. List all the proper subsets of {0,{1},3}.

    Text Solution

    |

  3. If a cosA=b cos B, then prove that either the triangle is isosceles or...

    Text Solution

    |

  4. If secx=sqrt(2) and x does not lie in the 1^(st) quadrant, find the va...

    Text Solution

    |

  5. Solve 4cos^(2)x=3,0lexle2pi

    Text Solution

    |

  6. For the quadratic equation (k-1)x^(2)-kx+1=0, find k so that the roots...

    Text Solution

    |

  7. Find the greatest value of 3+5x-2x^(2).

    Text Solution

    |

  8. A function f is defined on the set of real numbers as follows : f(x)...

    Text Solution

    |

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

    Text Solution

    |

  10. If alpha and beta are two different values of theta lying between 0 an...

    Text Solution

    |

  11. Using principle of mathematical induction, prove that 5^(n+1)+4.6^(n) ...

    Text Solution

    |

  12. Given that y=(3x-1)^(2)+(2x-1)^(3), find (dy)/(dx) and points on the c...

    Text Solution

    |

  13. Differentiate using 1^(st) principle : f(x)=(1)/(sqrt(2x+3))

    Text Solution

    |

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

    Text Solution

    |

  15. If the A.M. and G.M. between two numbers are in the ratio x:y, then pr...

    Text Solution

    |

  16. Prove that ((i-sqrt(3))/(i+sqrt(3)))^(100)+((i+sqrt(3))/(i-sqrt(3)))^(...

    Text Solution

    |

  17. The point P(-1,0) lies on the circle x^(2)+y^(2)-4x+8y+k=0. Find the r...

    Text Solution

    |

  18. A line is drawn through the point A(4,-1) and parallel to the line 3x-...

    Text Solution

    |

  19. Lives of LG and Samsung Microwaves that are currently popular were obs...

    Text Solution

    |