Home
Class 11
MATHS
Show that sin^2 5^0+sin^2 10^0+sin^2 15^...

Show that `sin^2 5^0+sin^2 10^0+sin^2 15^0+....+sin^2 90^0=9 1/2dot`

Text Solution

Verified by Experts

LHS
`=sin^2 5+sin^2 10+sin^2 15+...+sin^2 50`
`=(sinn^2 5+cos^2 5)+(sin^2 10+cos^2 10)+...+1/2+1`
`=(1+1+1+1+1+1+1+1+1)+1/2+1`
`=9+1/2=19/2`
RHS.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Show that sin^2 3^0+sin^2 6^0+sin^2 9^0++sin^2 90^0=15 1/2dot

sin^2 5^@+sin^2 10^@ + sin^2 15^@+.........+sin^2 85^@+sin^2 90^@ equals to

If 0^@ sin^2 theta .

Prove that 2sin2^0+4sin4^0+6"sin"6^0+.......+180sin180^0=90cot1^0dot

The value of sin^2 12^0+sin^2 21^0+sin^2 39^0+sin^2 48^0-sin^2 9^0-sin^2 18^0 is _______

Show that sin^(2) 12^(@)+ sin ^(2)21^(@)+ sin ^(2)39^(@)+ sin^(2)48^(@)=1+ sin^(2)9^(@)+ sin^(2)18^(@)

Show that |[cos 15^@ sin 15^@],[sin 75^@ cos 75^@]| =0

sin2x + sin4x + sin6x=0

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

The value of the expression (tan^2 20^0-sin^2 20^0)/(tan^2 20^0+sin^2 20^0) is__________

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the value of 2cos^3(pi/7)-cos^2(pi/7)-cos(pi/7)

    Text Solution

    |

  2. In acute angled triangle A B C ,A D is the altitude. Circle drawn with...

    Text Solution

    |

  3. Show that sin^2 5^0+sin^2 10^0+sin^2 15^0+....+sin^2 90^0=9 1/2dot

    Text Solution

    |

  4. Solve (sin^3x/2-cos^3x/2)/(2+sinx)=(cosx)/3

    Text Solution

    |

  5. Prove that 4cos(2pi)/7dotcospi/7-1=2cos(2pi)/7dot

    Text Solution

    |

  6. Suppose alpha,beta,gammaa n ddelta are the interior angles of regular ...

    Text Solution

    |

  7. Find the value of cos^2pi/(16)+cos^2(3pi)/(16)+cos^2(5pi)/(16)+cos^2(7...

    Text Solution

    |

  8. Solve (sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(5)))/(cosx)=8,x in (0,pi/2)

    Text Solution

    |

  9. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15...

    Text Solution

    |

  10. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

    Text Solution

    |

  11. If sin(120° – α) = sin(120° – β) and 0 < α, β < π then find the relati...

    Text Solution

    |

  12. Solve cosxcos2xcos3x=1/4

    Text Solution

    |

  13. Prove that sin 6^@ sin 42^@sin 66^@sin 78^@=1/16

    Text Solution

    |

  14. If the since of the angles A and B of a triangle ABCsatisfy the equati...

    Text Solution

    |

  15. Find the sign of the values of tan113^0-cos107^0=a and tan107^0-cos105...

    Text Solution

    |

  16. Solve the equation (sqrt(3))/2sinx-cosx=cos^2x

    Text Solution

    |

  17. Each question contains statements given in two columns which have to b...

    Text Solution

    |

  18. If xsina+ysin2a+zsin3a=sin4a, xsinb+ysin2b+zsin3b=sin4b, xsinc+ysin2...

    Text Solution

    |

  19. Prove that (sinx-cosx+1)/(sinx+cosx-1)=secx+tanx

    Text Solution

    |

  20. The lengths of the medians through acute angles of a right-angled tr...

    Text Solution

    |