Home
Class 11
MATHS
Evaluate the following: sin 78^0cos 18^0...

Evaluate the following: `sin 78^0cos 18^0-cos 78^0sin 18^0`

Text Solution

Verified by Experts

Given,`sin 78^ocos 18^o-cos 78^osin 18^o`
=`sin(78^o-18^o)`
=`sin(60^o)`
=`sqrt(3)/2`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following: sin 78^@ cos 18^@-cos 78^@ sin 18^@

Evaluate the following: cos47^(0)cos13^(0)-sin47^(0)sin13^(@)

Evaluate the following: sin36^(@)cos9^(0)+cos36^(@)sin9^(0)

Evaluate the following: sin39^0-cos51^0 (ii) cos e c25^0-sec65^0 cot34^0-tan56^0 (iv) (sin36^0)/(cos54^0)-(sin54^0)/(cos36^0) cos^2 13^0-sin^2 77^0

Find the values of the following: sin75^0 (ii) cos75^0 (iii) sin15^0 (iv) cos15^0

Without using trigonometric tables, evaluate the following: (sec37^0)/(cos e c53^0)+2cot15^0cot25^0cot45^0cot75^0cot65^0(sin^2 18^0+sin^2 72^0)

(2cos 40^0-cos 20^0)/(sin 20^0)=

Evaluate : (sin 18^(@))/(cos 72^(@))

If cos x=tan y,cos y=tan z,cos z=tan x then the value of sin x is (a)2cos18^(0)(b)cos18^(0)(c)sin18^(0)(d)2sin18^(@)

Find the value of x in each of the following: (i)tan3x=sin45^0cos45^0+sin30^0, (ii)cosx=cos60^0cos30^0+sin60^0sin30^0 , (iii)sin2x=sin60^0cos30^0-cos60^0sin30^0dot

RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If sinA=1/2,cosB=(sqrt(3))/2,\ w h e r e\ pi/2<A<pi\ a n d\ 0<B<pi/2 ,...

    Text Solution

    |

  2. If sinA=1/2,cosB=(sqrt(3))/2, w here pi/2 lt A lt pi and 0ltBltpi/2 f...

    Text Solution

    |

  3. Evaluate the following: sin 78^0cos 18^0-cos 78^0sin 18^0

    Text Solution

    |

  4. Evaluate the following: sin 36^0cos9^0+cos36^0 sin9^0

    Text Solution

    |

  5. Evaluate the following: cos 47^0cos 13^0-sin 47^0 sin 13^0

    Text Solution

    |

  6. Evaluate the following: cos 80^0cos 20^0+ sin 80^0 sin 20^0

    Text Solution

    |

  7. If cos A=-12/13 and cotB=24/7 where A lies in second quadrant and B li...

    Text Solution

    |

  8. Prove that: cos 105^@+cos15^@=sin 75^@-sin 15^@

    Text Solution

    |

  9. (tanA+tanB)/(tanA-tanB)=sin(A+B)/(sin(A-B)

    Text Solution

    |

  10. Prove that: (cos 11^@+"sin"11^@)/(cos 11^@-"sin"11^@)=tan 56^@

    Text Solution

    |

  11. Prove that: (cos8^@-"sin"8^@)/(cos8^@+"sin"8^@)=t a n 37^@

    Text Solution

    |

  12. (cos9^@+sin9^@)/(cos9^@-sin9^@)= (a) tan 54^@ (b) tan 36^@ (d) None of...

    Text Solution

    |

  13. Prove that: sin(60^0-theta)-cos(30^0+theta)=0.

    Text Solution

    |

  14. Prove that: sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt...

    Text Solution

    |

  15. Prove that: sin((3"pi")/8-5)cos("pi"/8+5)+cos((3"pi")/8-5)sin("pi"/8+7...

    Text Solution

    |

  16. Prove that :(tan69^@+tan 66^@)/(1-tan 69^@tan66^@)=-1

    Text Solution

    |

  17. If tanA=5/6 and tanB=1/(11),\ p rov e\ t h a t\ A+B=pi/4

    Text Solution

    |

  18. If tanA=m/(m-1)\ and tanB=1/(2m-1), then prove that A-B=\ pi/4

    Text Solution

    |

  19. Prove that: cos^2 45^@-sin^2 15^@=(sqrt(3))/4

    Text Solution

    |

  20. Prove that: sin^2(n+1)A-sin^2n A="sin"(2n+1)A s in A

    Text Solution

    |