Home
Class 11
MATHS
In a right angled triangle ABC, write th...

In a right angled triangle ABC, write the value of `sin^2 A + sin^2 B+ sin^2C`

Text Solution

Verified by Experts

Let `C=90^@`
Then,
`sin^2A+sin^2B+sin^2C`
=`sin^2A+sin^2B+sin^2(90)`
=`sin^2A+sin^2B+1`
=`sin^2A+sin^2(π/2​−A)+1`
=`sin^2A+cos^2A+1`
=`1+1=2`
Promotional Banner

Topper's Solved these Questions

  • SETS

    RD SHARMA|Exercise Solved Examples And Exercises|218 Videos

  • SOME SPECIAL SERIES

    RD SHARMA|Exercise Solved Examples And Exercises|69 Videos

Similar Questions

Explore conceptually related problems

In a right angled triangle ABC,write the value of sin^(2)A+sin^(2)B+sin^(2)C

In a triangle ABC, the value of sin A+sin B+sin C is

In triangle ABC,the value of sin2A+sin2B+sin2C is equal to

In a Delta ABC, right angled at B, what is the value of 2 sin A cot A if tanA=sqrt3 .

If A, B, C are angle of a triangle ABC, then the value of the determinant |(sin (A/2), sin (B/2), sin (C/2)), (sin(A+B+C), sin(B/2), cos(A/2)), (cos((A+B+C)/2), tan(A+B+C), sin (C/2))| is less than or equal to

In any Delta ABC the maximum value of (sin^(2)A+sin^(2)B+sin^(2)C) is

If Delta ABC is right-angled triangle,then sum(sin^(2)A) is

In triangle ABC , prove that b^2sin2C+c^2sin2B=2bcsinA .

If Delta ABC is right angled at B then what is the value of sin(A+C)

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. In a DeltaA B C , if (c+a+b)(a+b-c)=a b , then the measure of angel C...

    Text Solution

    |

  2. If any triangle A B C , that: (b^2-c^2)/(cosB+cosC)+(c^2-a^2)/(cosC+co...

    Text Solution

    |

  3. In a right angled triangle ABC, write the value of sin^2 A + sin^2 B+ ...

    Text Solution

    |

  4. If any triangle A B C , that: (asin(B-C))/(b^2-c^2)=(bsin(C-A))/(c^2-...

    Text Solution

    |

  5. In a Delta A B C , if cosC=(sinA)/(2sinB) , prove that the triangle is...

    Text Solution

    |

  6. Problem on sine rule Type:-2 (i)The angle of elevation of the top of ...

    Text Solution

    |

  7. (sqrt(sinA)-sqrt(sinB))/(sqrt(sinA)+sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b...

    Text Solution

    |

  8. The angle of elevation of the top of a tower from a point A due south ...

    Text Solution

    |

  9. (bsecB+csecC)/(tanB+t a n C)=(csecC+asecA)/(tanC+t a n A)=(asecA+bsecB...

    Text Solution

    |

  10. a(cosC-cosB)=2(b-c)cos^2A/2

    Text Solution

    |

  11. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

    Text Solution

    |

  12. cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2

    Text Solution

    |

  13. In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B

    Text Solution

    |

  14. In any triangle A B C , prove that: (sin(B-C))/(sin(B+C))=(b^2-c^2)/(a...

    Text Solution

    |

  15. In any triangle A B C , prove that: \ asin(B-C)+b s in(C-A)+csin(A-B)=...

    Text Solution

    |

  16. In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...

    Text Solution

    |

  17. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

    Text Solution

    |

  18. In any triangle A B C , prove that: (b-c)/(b+c)=(tan((B-C)/2))/(tan((B...

    Text Solution

    |

  19. In any triangle A B C , prove that: acos((B+C)/2)=(b+c)sinA/2

    Text Solution

    |

  20. A tree stands vertically on a hill side which makes an angle of 15^0 w...

    Text Solution

    |