Home
Class 12
MATHS
sin^(2)5^@+sin^(2)10^@+sin^(2)15^@ +.......

`sin^(2)5^@+sin^(2)10^@+sin^(2)15^@ +.......+sin^(2)85^@ + sin^(2)90^@=`

A

7

B

8

C

9

D

`(19)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(2)5^(@)+sin^(2)10^(@)+sin^(2)15^(@)+.........+.........+sin^(2)75^(@)+sin^(2)80^(@)+sin^(2)85^(@)+sin^(2)90^(@)`
`rArrsin^(2)5^(@)+sin^(2)10^(@)+sin^(2)15^(@)+.......sin^(2)(90-15^(@))+sin^(2)(90-10)+sin^(2)(90-5)+1`
`rArrsin^(2)5+sin^(2)10+sin^(2)15^(@)+.......+cos^(2)15^(@)+cos^(2)10^(@)+cos^(2)5^(@)+1`
`rArr(1+1+1+....8" times")_=+sin^(2)45^(@)+1`
`rArr8+(1)/(2)+1=(19)/(2)`
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    NDA PREVIOUS YEARS|Exercise MCQs|204 Videos

  • VECTORS

    NDA PREVIOUS YEARS|Exercise MATH|199 Videos

Similar Questions

Explore conceptually related problems

sin^2 75^@-sin^2 15^@ =

sin^(2)5^(@) + sin^(2)25^(@) + sin^(2)45^(@) + sin^(2) 65^(@) + sin^(2) 85^(@) is equal to:

sin^(2) 75^(@) - sin^(2)15^(@)=

The value of sin^2 5^@ + sin^2 10^@ + sin^2 15^@ + sin^2 20^@ + ... + sin^2 90^@ is:

The value of sin^(2) 1^(@) + sin^(2) 2^(@) + sin^(2) 3^(@)+ . . . . + sin^(2) 89^(@) + sin ^(2) 90^(@) is

(sin^(2)1^(@) + sin^(2)3^(@) + sin^(2)5^(@) +sin^(2)7^(@) + ….. + sin^(2)87^(@) + sin^(2)89^(@)) equals

The value of the expression sin^(2)1^(@)+sin^(2)11^(@)+sin^(2)21^(@)+ sin^(2)31^(@)+sin^(2)41^(@)+sin^(2)45^(@)+ sin^(2)49^(@)+sin^(2)59^(@)+sin^(2)69^(@)+ sin^(2)79^(@)+sin^(2)89^(@) is :

Find the value of sin^(2)5^(@)+ sin^(2)10^(@)+ sin^(2)15^(@)+* * * +sin^(2)90^(@) .

The numerical value of sin^(2)5^circ + sin^(2)10^circ + sin^(2)15^circ + . . . + sin^(2)90^circ=.........

NDA PREVIOUS YEARS-TRIGONOMETRY - RATIO & IDENTITY , TRIGONOMETRIC EQUATIONS-MCQ
  1. (1-sinA+cosA)^(2) is equal to ?

    Text Solution

    |

  2. What is (costheta)/(1-tantheta)+(sin theta)/(1-cottheta) equal to ?

    Text Solution

    |

  3. sin^(2)5^@+sin^(2)10^@+sin^(2)15^@ +.......+sin^(2)85^@ + sin^(2)90^@=

    Text Solution

    |

  4. Prove that: (cos^(3)A-cos3A)/(cosA)+(sin^(3)A+sin3A)/(sinA)=3

    Text Solution

    |

  5. If sin x + sin y = a and cos x + cos y=b, then tan^2\ (x+y)/2 + tan^2\...

    Text Solution

    |

  6. Consider a triangle ABC satisfying 2asin^(2)((C)/(2))+2csin^(2)((...

    Text Solution

    |

  7. Consider a triangle ABC satisfying 2asin^(2)((C)/(2))+2csin^(2)((...

    Text Solution

    |

  8. If p=tan(-(11pi)/(6)),q=tan((21pi)/(4))and r = cot ((283pi)/(6)), the...

    Text Solution

    |

  9. Given that tan alpha and tan beta are the roots of the equation x^(2...

    Text Solution

    |

  10. Given that tan alpha and tan beta are the roots of the equation x^(2...

    Text Solution

    |

  11. If A=(cos12^(@)-cos36^(@))(sin96^(@)+sin24^(@)) and B=(sin60^(@)-...

    Text Solution

    |

  12. sin A + 2 sin 2 A + sin 3 A is equal to which of the following ? 1...

    Text Solution

    |

  13. If x=sin70^(0). sin50^(0)and y = cos60^(@). cos80^(0), then what is x...

    Text Solution

    |

  14. If sintheta(1)+sintheta(2)+sintheta(3)+sintheta(4)=4, then what is t...

    Text Solution

    |

  15. (1+cos.(pi)/(8))(1+cos.(3pi)/(8))(1+cos.(5pi)/(8))(1+cos.(7pi)/(8)) is...

    Text Solution

    |

  16. If xcostheta+ysintheta=z, then what is the value of (xsintheta-ycos...

    Text Solution

    |

  17. If sin 18^@=(sqrt(5)-1)/4 then what is the value of sin 81^@

    Text Solution

    |

  18. (1-tan 2^0 cot 62^0)/( tan 152^0-cot 88^o) (a)sqrt3 (b)-sqrt3 (c) sqr...

    Text Solution

    |

  19. If sinA=(3)/(5)"where "450^(@)ltAlt540^(@),then "cos"(A)/(2) is equal ...

    Text Solution

    |

  20. 1/ (si n1 0^(@)) -(sqrt(3))/ (cos1 0^(@))=

    Text Solution

    |