Home
Class 12
MATHS
Prove that (sin20^(@) + sin40^(@)) + (co...

Prove that `(sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)`

Text Solution

Verified by Experts

LHS `=(sin 20^(@) + sin40^(@)) + (cos 20^(@)+ cos 40^(@))`
We know that, `sin C + sinD=2sin(C+D)/2 cos(C-D)/2`
and, `cosC + cosD = 2cos(C+D)/2 .cos(C-D)/2`.
Now, LHS `=2sin60^(@)/2. cos20^(@)/2+ 2cos60^(@)/2 . Cos20^(@)/2`.
`=cos10^(@) + sqrt(3)cos10^(@)`
`=(sqrt(3)+1) cos10^(@)`= R.H.S.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Try Yourself|32 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment section-A (Objective Type Questions (One option is correct))|49 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - J|10 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise SECTION-J (Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

(sin 70^(@) + cos 40^(@))/(cos 70^(@) + sin 40^(@))=

Prove that :(cos20^(@)-sin20^(@))/(cos20^(@)+sin20^(@))=tan25^(@)

(cos30^(@)-sin20^(@))/(cos40^(@)+cos20^(@))=(4)/(sqrt(3))cos40^(@)cos80^(@)

sin20^(@)*cos40^(@)+cos20^(@)*sin40^(@)=(sqrt(3))/(2)

cos70^(@)+sin40^(@)=

cos 20^(@) cos 40^(@) cos 80^(@)=

Prove that (i) sin 70^(@) cos 10^(@) -cos 70^(@) sin 10^(@) =(sqrt(3))/(2) (ii) cos 50^(@) cos 10^(@) -sin 50^(@) sin 10^(@) =(1)/(2) (ii) cos 80^(@) cos 20^(@) + sin 80^(@) sin 20^(@) =(1)/(2) (iv) sin 36^(@) cos 9^(@) + cos 36^(@) sin 9^(@) =(1)/(sqrt(3))

Prove that: cos20^(@)cos40^(@)cos80^(@)=(1)/(8)

(cos20^(@)-sin20^(@))/(cos20^(@)+sin20^(@))=tan25^(@)

(sin70^(@)+cos40^(@))/(cos70^(@)+sin40^(@))=

AAKASH INSTITUTE-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
  1. Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+...

    Text Solution

    |

  2. If cos^(2009)x(1) + cos^(2009)x(2) + cos^(2009)x(3) + ………. +cos^(2009)...

    Text Solution

    |

  3. If acos^3alpha+3acosalphasin^2alpha=m, asin^3alpha+3acos^2alphasinalph...

    Text Solution

    |

  4. If alpha satisfies 15 sin^(4)alpha + 10 cos^(4)alpha=6, then find the ...

    Text Solution

    |

  5. If A= tan27theta - tantheta and B= (sintheta)/(cos 3theta) +(sin 3thet...

    Text Solution

    |

  6. If A=sqrt(3) cot 20^(@) - 4 cos20^(@) and B= sin12^(@) sin48^(@) sin54...

    Text Solution

    |

  7. If tan alpha = 1/sqrt(x(x^2+x+1)),tan beta=sqrtx/sqrt(x^2+x+1) and ...

    Text Solution

    |

  8. The number of values of x lying in [-pi, pi] and satisfying 2sin^2the...

    Text Solution

    |

  9. The number of solutions of the equation sin^(5)theta + 1/(sintheta) = ...

    Text Solution

    |

  10. The number of solutions of x in the interval [-pi, pi] of the equation...

    Text Solution

    |

  11. The general solution of the equation tan(x+20^@)tan(x-4 0^(@))=tan(x-...

    Text Solution

    |

  12. Let x it [0,2pi] The curve y=secx tanx +2tanx - sec x and the line y=0...

    Text Solution

    |

  13. Let the number of solutions of the equations sinx =x^(2) - 4x +5 be la...

    Text Solution

    |

  14. Let three sets be defined as A={x|cos2x + cosx+1=0} B={x|cos2x + 3...

    Text Solution

    |

  15. The number of solutions of the equation 2^|x|=1+2|cosx| is

    Text Solution

    |

  16. If the equation 1 +sin^2 xtheta= costheta has a non-zero solution in t...

    Text Solution

    |