Home
Class 11
MATHS
If sin^(2).(A)/(2)+sin^(2).(B)/(2)+sin^(...

If `sin^(2).(A)/(2)+sin^(2).(B)/(2)+sin^(2).(C)/(2)` are in H.P , show that a , b, c are in H. P

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(a), (1)/(b) , (1)/ (c )` are in A.P. `rArr a,b,c` are in H.P.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(b) ) I.|5 Videos

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(b) ) II.|6 Videos

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(a) ) II.|14 Videos

  • PRODUCT OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise SOLVED PROBLEMS|46 Videos

  • STRAIGHT LINE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-3(e)) |32 Videos

Similar Questions

Explore conceptually related problems

If A, B , C are angles of a triangle, then P. T sin ^(2) . (A)/(2)+ sin^(2). (B)/(2) - sin ^(2). (C)/(2) =1-2 cos. (A)/(2) cos. (B)/(2) sin .(C)/(2)

If (1)/(a^(2)), (1)/(b^(2)), (1)/(c^(2)) are in H.P., then

If A+B+C=180^@ " then " sin^(2)""(A)/(2)-sin^(2)""(B)/(2)+sin^(2)""(C)/(2)=

If 2 sin ""( A) /( 2) sin ""( C)/(2) = sin "" ( B) /(2) then a,b,c are in

In Delta ABC, if sin^2""A/2, sin^2""B/2,sin^2""C/2 are in H.P, then a,b,c in

In a DeltaABC , if "tan"(A)/(2),"tam"(B)/(2),"tan"(C)/(2) are in H.P then a,b,c, are in

If sin ^(2) A+ sin ^(2) B + sin ^(2) C then angle C =

If A+B+C=180^(@) " then " sin^(2)""(A)/(2)+sin^(2)""(B)/2+sin^(2)""(C)/(2)=

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PROPERTIES OF TRIANGLES-TEXTUAL EXERCISES ( EXERCISE - 10(a) ) III.
  1. In Delta ABC, sum (a+b) tan ((A-B)/2)=

    Text Solution

    |

  2. b-c // b+c cot A/2 + b+c // b-c tan A/2 = 2 cosec (B-C)అని చూపండి.

    Text Solution

    |

  3. If sin theta = a/(b+c) then show that cos theta = (2sqrt(bc))/(b+c) co...

    Text Solution

    |

  4. If a=(b+c)costheta, " then prove that" sintheta=(2sqrt(bc))/(b+c)cos((...

    Text Solution

    |

  5. In Delta ABC, b cos (C+ theta)+c cos (B- theta)=

    Text Solution

    |

  6. If the angles of triangles ABC are in A.P. and b: c= sqrt3 : sqrt2 "...

    Text Solution

    |

  7. If (a^(2)+b^(2))/(a^(2)-b^(2))=(sinC)/(sin(A-B)) , then S.T . DeltaAB...

    Text Solution

    |

  8. In Delta ABC, if cos A+cos B+ cos C=3//2, then the triangle is

    Text Solution

    |

  9. If cos ^(2) A + cos ^(2) B = cos ^(2) C = 1 then show that Delta A...

    Text Solution

    |

  10. In a /\ABC if a^(2)+b^(2)+c^(2)=8R^(2) then show that/\ABC is a right ...

    Text Solution

    |

  11. In Delta ABC , if cot "" (A)/(2) , cot "" ( B)/(2) , cot "" (C )/(2...

    Text Solution

    |

  12. If sin^(2).(A)/(2)+sin^(2).(B)/(2)+sin^(2).(C)/(2) are in H.P , show t...

    Text Solution

    |

  13. C=90^(0) అయితే, (a^(2) + b^(2) // a^(2) - b^(2)) sin (A- B) =1 అని నిర...

    Text Solution

    |

  14. a^(2) sin 2C + c ^(2) sin 2A =

    Text Solution

    |

  15. A lamp post is sittuated at the middle point M of the side AC of a tri...

    Text Solution

    |

  16. Two ships leave a port at the same time . One goes 24km per hour in th...

    Text Solution

    |

  17. A tree stands vertically on the slant of the hills From a point A on t...

    Text Solution

    |

  18. The upper 3//4^(th) portion of a vertical pole subtends an angle "Tan"...

    Text Solution

    |

  19. AB is vertical pole with B at ground level and A at the top. A man fi...

    Text Solution

    |

  20. Let an object be placed at some height h cm and let P and Q two points...

    Text Solution

    |