Home
Class 12
MATHS
In DeltaABC If, (sin^2A+sin^2B+sin^2C)/(...

In `DeltaABC` If, `(sin^2A+sin^2B+sin^2C)/(cos^2A+cos^2B+cos^2C)`=2 Then the triangle is

A

right-angled

B

equilateral

C

isosceles

D

obtuse-angled

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(sin^(2)A+sin^(2)B+sin^(2)C)/(cos^(2)A+cos^(2)B+cos^(2)C)=2`.
Let us take `A = 30^(@), B = 60^(@), C = 90^(@)`
`(sin^(2)30^(@)+sin^(2)60^(@)+sin^(2)90^(@))/(cos^(2)30^(@)+cos^(2)60^(@)+cos^(2)90^(@))`
`=((1)/(4)+(3)/(4)+1)/((3)/(4)+(1)/(4)+0)=(1+1)/(1)=(2)/(1)=2`.
So, the given triangle is right-angled triangle.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY AND PROBABILIYT DISTRIBUTION

    NDA PREVIOUS YEARS|Exercise Multiple Choice Question|213 Videos

  • QUESTION PAPER 2021

    NDA PREVIOUS YEARS|Exercise MULTIPLE CHOICE QUESTIONS|120 Videos

Similar Questions

Explore conceptually related problems

In Delta ABC If,(sin^(2)A+sin^(2)B+sin^(2)C)/(cos^(2)A+cos^(2)B+cos^(2)C)=2 Then the triangle is

In a DeltaABC , If (Sin^(2)A+Sin^(2)B+Sin^(2)C)/(Cos^(2)A+Cos^(2)B+Cos^(2)C)=2 then the triangle is

If in a DeltaABC, sin A =sin^(2) B and 2 cos ^(2)A=3 cos ^(2) B, then the DeltaABC is

In Delta ABC, if sin A+sin B+sin B+sin C=1+sqrt(2) and cos A+cos B+cos C=sqrt(2) then the triangle is

If in a Delta ABC, cos B = (sin A)/(2 sin C), then the triangle is

If a triangle ABC, sin A = sin^(2) B and 2 cos^(2)A = 3 cos^(2)B , then the Delta ABC is :

Statement-1: In a triangle ABC, if sin^(2)A + sin^(2)B + sin^(2)C = 2 , then one of the angles must be 90 °. Statement-2: In any triangle ABC cos 2A + cos 2B + cos 2C = -1 - 4 cos A cos B cos C

In a !ABC , sin A + sin B + sin C = 1+ sqrt2 and ,cos A +cos B +cos C = sqrt2 if ,the triangle is

NDA PREVIOUS YEARS-PROPERTIES OF TRIANGLE, INVERSE TRIGONOMETRIC FUNCTION-MCQ
  1. Consider the following statements : 1. tan^(-1) x + tan^(-1)((1)/(x)...

    Text Solution

    |

  2. Consider the following statement : 1. If ABC is an equilateral trian...

    Text Solution

    |

  3. The value of cos (2Cos^-1 0.8) is

    Text Solution

    |

  4. Consider the following for triangle ABC : 1. sin((B+C)/(2))=cos((A)/...

    Text Solution

    |

  5. The value of sin^(-1)((3)/(5))+tan^(-1)((1)/(7)) is equal to

    Text Solution

    |

  6. In a triangle ABC, a-2b +c=0.The value of cot(A/2)cot(C/2) is

    Text Solution

    |

  7. In DeltaABC If, (sin^2A+sin^2B+sin^2C)/(cos^2A+cos^2B+cos^2C)=2 Then t...

    Text Solution

    |

  8. The principal value of sin^(-1) x lies in the interval

    Text Solution

    |

  9. In a triangle ABC if a = 2, b = 3 and sin A = (2)/(3), then what is an...

    Text Solution

    |

  10. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

    Text Solution

    |

  11. If x, x - y and x + y are the angles of a triangle (not an equilateral...

    Text Solution

    |

  12. ABC is a triangle inscribed in a circle with centre O. Let alpha = ang...

    Text Solution

    |

  13. What is tan^(-1)((1)/(4))+tan^(-1)((3)/(5)) equal to ?

    Text Solution

    |

  14. If A + B + C = 180^(@), then what is sin 2A - sin 2N - sin 2C equal to...

    Text Solution

    |

  15. Consider the following values of x : 1. 8 2. -4 3. (1)/(6) 4. ...

    Text Solution

    |

  16. Let the slope of the curve y = cos^(-1) (sin x) be tan theta : Then th...

    Text Solution

    |

  17. What is the value of "sin"^(-1)(4)/(5)+"sec"^(-1)(5)/(4)-(pi)/(2)?

    Text Solution

    |

  18. if sin^-1((2p)/(1+p^2))-cos^-1((1-q^2)/(1+q^2))=tan^((2x)/(1-x^2)) pr...

    Text Solution

    |

  19. If in triangle the angles be to the one another as 1:2:3 , prove that ...

    Text Solution

    |

  20. What is the derivative of sec^(2)(tan^(-1)x) with respect to x ?

    Text Solution

    |