Home
Class 12
MATHS
Prove that: sin(-420^0)(cos390^0)+cos(-6...

Prove that: `sin(-420^0)(cos390^0)+cos(-660^0)(s in330^0)=-1.`

Text Solution

Verified by Experts

`L.H.S.=sin(-420^@)(cos390^@)+cos(-660^@)(sin330^@)`
`=-sin420^@cos390^@+cos660^@sin330^@`
`[ :' sin(-theta)=-sintheta,cos(-theta)=costheta]`
`=-sin(90^@xx4+60^@)cos(90^@xx4+30^@)`
`+cos(90^@xx7+30^@)sin(90^@xx3+60^@)`
`=-(sin60^(@))(cos30^@)+(sin30^@)(-cos60^@)`
`=-sqrt3/2xxsqrt3/2+1/2(-1/2)=-1=R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.1|8 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.2|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Prove that: sin(-420^(@))cos390^(@)+cos(-660^(@))sin330^(@)=1

Prove that: sin(-420^(@))(cos390^(@))+cos(-660^(@))(sin330^(@))=-1

Prove that sin(-420^(@))(cos390^(@))+cos(-660^(@))(sin330^(@))=-1

Prove that: sin420^(@)cos390^(@)+cos(-300^(@))sin(-330^(@))=1

Prove that: "sin"420^(@) cos390^(@)+cos(-660^(@))"sin"(-390^(@))=(1)/(2) .

Prove that: s in47^(0)+cos77^(0)=cos17^(0)

Prove that: sin600^(@)cos390^(@)+cos480^(@)s in150^(@)=-1

Prove that: s in23^(0)+s in37^(0)=cos7^(0)

Prove that :sin51^(0)+cos81^(0)=cos21^(0)

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

CENGAGE-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(s in330^0)=-1.

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. sintheta/(1-cottheta)+costheta/(1-tantheta)= (a)theta (b)1 (c)costh...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. The value of (tan^(2)20^(@)-sin^(2)20^(@))/(tan^(2)20^(@).sin^(2)20^(@...

    Text Solution

    |

  6. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

    Text Solution

    |

  7. In DeltaABC, if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cos...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4) is equal...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is

    Text Solution

    |

  12. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

    Text Solution

    |

  13. If x,y,z be all positive acute angles then the least value of tanx(cot...

    Text Solution

    |

  14. Three circles each of radius 1, touch one another externally and they ...

    Text Solution

    |

  15. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |