Home
Class 11
MATHS
Prove that: sin 65^0+cos 65^0=sqrt(2)cos...

Prove that: `sin 65^0+cos 65^0=sqrt(2)cos 20^0`

Text Solution

Verified by Experts

We have to proof,
`sin(65^o)+cos(65^o)=sqrt(2)cos(20^o)`
Let,
L.H.S.=`sin(65^o)+cos(65^o)`
L.H.S=`sin(65^o)+cos((90^o)-(25^o))`
L.H.S=`sin(65^o)+sin(25^o)`
As we know the formula,
`sin(A^o)+sin(B^o)= 2[sin(((A^o) +(B^o))/2)cos(((A^o)-(B^o))/2)]`
then, L.H.S=`sin(65^o)+sin(25^o)`
...
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

Similar Questions

Explore conceptually related problems

(a) Prove that sin65^(@)+cos65^(@)=sqrt(2)cos 20^(@) (b) Prove that sin47^(@)+cos77^(@)=cos17^(@)

sin65^(@)+cos65^(@)=sqrt(2)cos20^(@)

2sin65^@cos25^@=

Prove that cos65^(@)+cos115^(0)=0

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

Prove that : "cosec "65^(@)cos25^(@)+"cosec20"^(@)cos70^(@)=2

Prove that: cos55^(@)+cos65^(0)+cos175^(0)=0

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that: cos18^(@)-sin18^(0)=sqrt(2)sin27^(0)

Prove that: sin^(2)42^(0)-cos^(2)78^(0)=(sqrt(5)+1)/(8)

RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Prove that: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt(2)sinx

    Text Solution

    |

  2. Prove that: cos(pi/4+x)+cos(pi/4-x)=sqrt(2)\ cos x

    Text Solution

    |

  3. Prove that: sin 65^0+cos 65^0=sqrt(2)cos 20^0

    Text Solution

    |

  4. Prove that: sin 47^0+cos 77^0=cos 17^0

    Text Solution

    |

  5. Prove that: cos3A+cos5A+cos7A+cos 15 A=4cos4A cos5A cos6A

    Text Solution

    |

  6. Prove that: \ cos A+cos3A+cos5A+cos7A=4cos A cos2A cos4A

    Text Solution

    |

  7. Prove that sinA+sin2A+sin4A+sin5A=4 (cosA/2)(cos3A/2)sin3A

    Text Solution

    |

  8. Prove that: cos 20^0cos 100^0+cos 100^0cos 140^0-\ cos 140^0cos 200^0=...

    Text Solution

    |

  9. Prove that: \ sin3A+sin2A-sin A=4sin A cos A/2cos3A/2

    Text Solution

    |

  10. Prove that:costhetacostheta/2-cos3thetacos(9theta)/2=sin7theta\ sin8th...

    Text Solution

    |

  11. Prove that: (sin A+sin3A)/(cos A-cos3A)=cotA

    Text Solution

    |

  12. Prove that: (sin9A-sin7A)/(cos7A-cos9A)=cot8A

    Text Solution

    |

  13. Prove that: (sin A-sin B)/(cos A+cos B)=tan((A-B)/2)

    Text Solution

    |

  14. Prove that: (sin A+sin B)/(sin A-sin B)=tan((A+B)/2)cot((A-B)/2)

    Text Solution

    |

  15. Prove that: (cos A+cos B)/(cos B-cos A)=cot((A+B)/2)cot((A-B)/2)

    Text Solution

    |

  16. Prove that:(sinA+sin3A+sin5A)/(cos A+cos3A+cos5A)=tan3A

    Text Solution

    |

  17. Prove that: (cos3A+2cos5A+cos7A)/(cos A+2cos3A+cos5A)=(cos5A)/(cos3A)

    Text Solution

    |

  18. Prove that: (cos4A+cos3A+cos2A)/(sin4A+sin3A+sin2A)=cot3A

    Text Solution

    |

  19. Prove that: (sin3A+sin5A +sin7A+sin9A)/(cos3A+cos5A+cos7A+cos9A)=tan6A

    Text Solution

    |

  20. Prove that: (sin5A cos2A-sin6A\ cos A)/(sin A\ sin2A-cos2A cos3A)=t a ...

    Text Solution

    |