Home
Class 11
MATHS
In triangle ABC, if A - B = 120 and R = ...

In triangle ABC, if `A - B = 120 and R = 8r`, where R and r have their usual meaning, then cos C equals

Text Solution

Verified by Experts

`R = 8r`
`=>R = 8(4Rsin(A/2)sin(B/2)sin(C/2))`
`=>2sin(A/2)sin(B/2)sin(C/2) = 1/16`
`=>(cos((A-B)/2) - cos((A+B)/2))sinC/2 = 1/16`
As, `(A-B) = 120^@ and C = pi-(A+B),`
so, our equation becomes,
`=>(1/2-sin(C/2)) sin(C/2) = 1/16`
`=>sin(C/2) = 1/4`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, if a = 2 and bc = 9, then prove that R = 9//2Delta

Show that for 1 mole of an ideal gas C_p-C_v=R , where C_p and C_v have their usual meaning.

In the triangle ABC, if a=5, b=7 and c=3, find the angle B and the circumradius R.

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then b : c is equal to

In a triangle ABC, angleC=90^(@) , r and R are the in-radius and circum-radius of the triangle ABC respectively, then 2(r+R) is eqaul to

In a triangle ABC, angleC=90^@, r and R are the inradius and circumradius of the triangle ABC respectively, then 2(r+R) is equal to

In triangle A B C ,l e tR=c i r c u m r a d i u s ,r= i n r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to (a) sqrt(2)-1 (b) sqrt(3)-1 (c) sqrt(2)+1 (d) sqrt(3)+1

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to a+b (b) b+c c+a (d) a+b+c

If the incircle of the Delta ABC touches its sides at L , M and N and if x , y , z be thecircumradii of the triangles MIN , NIL and LIM respectively, where I is the incentre, then the product xyz is equal to: (A) R r^2 (B) r R^2 (C) 1/2R r^2 (D) 1/2r R^2

If 5, 5r and 5r^(2) are the lengths of the sides of a triangle, then r cannot be equal to

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. In triangle A B C ,l e tR=c i r c u m r a d i u s ,r= i n r a d i u ...

    Text Solution

    |

  2. The expression cos^2(alpha+beta)+cos^2(alpha-beta)-cos2alpha.cos2beta,...

    Text Solution

    |

  3. In triangle ABC, if A - B = 120 and R = 8r, where R and r have their u...

    Text Solution

    |

  4. The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=co...

    Text Solution

    |

  5. If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) ...

    Text Solution

    |

  6. Show that 16cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(1...

    Text Solution

    |

  7. A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are...

    Text Solution

    |

  8. The total number of solutions of loge |sin x| = -x^2 +2x in [0,pi] is...

    Text Solution

    |

  9. If sin^2theta1+sin^2theta2+sin^2theta3=0, then which of the following ...

    Text Solution

    |

  10. The length of the shadow of a vertical pole of height h , thrown by th...

    Text Solution

    |

  11. For real values of 'x' , Which of the following is/are always positiv...

    Text Solution

    |

  12. The total number of solution of sin{x}=cos{x} (where {} denotes the fr...

    Text Solution

    |

  13. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |

  14. If tan^3A+tan^3B+tan^3C=3tanA* tanB*tanC , then prove that triangle A...

    Text Solution

    |

  15. Find the value of x for which 3cosx=x^2-8x+19 holds good.

    Text Solution

    |

  16. The set of all x in ((-pi)/2,pi/2) satisfying |4sinx-1| < sqrt(5) ...

    Text Solution

    |

  17. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  18. Prove that tan 70^@=tan 20^@+2tan50^@

    Text Solution

    |

  19. Show that the equation sintheta=x+1/x is not possible if x is real.

    Text Solution

    |

  20. Solve: 2sin^2x+sin^2 2x=2

    Text Solution

    |