Home
Class 11
MATHS
Prove that (cosx+cosy)^2+(sinx-siny)^2=4...

Prove that` (cosx+cosy)^2+(sinx-siny)^2=4cos^2((x+y)/2)`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

Show that (cos x +cos y)^2 +(sinx+siny)^2=4 cos^2((x-y)/2)

Prove that (cos x-cos y)^(2)+(sin x-sin y)^(2)=4 sin ^(2)((x-y)/(2))

Prove that, (sinx+cosx)^2=1+sin2x

Prove that 1+cos 2x=2cos^2x .

Prove that cos^2 2x-cos^2 6x=sin4x sin8x

Prove that cos 4(x)=1-8 sin ^(2) (x) cos ^(2) (x)

Prove that (i) 2 cos x cos y=cos (x+y)+cos (x-y) (ii) -2 . sin x sin y=cos (x+y)-cos (x-y) (iii) 2 sin x cos y=sin (x+y)+sin (x-y) (iv) 2 cos x sin y=sin (x+y)-sin (x-y)

Prove that (sinx-siny)/(cosx+cosy)=tan(x-y)/2

Prove that sin3x+sin2x-sinx=4sinxcos(x/2)cos((3x)/2)

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

A N EXCEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Consider the trignometric equation 4cos^2theta+6sin^2theta=5 prove tha...

    Text Solution

    |

  2. Consider the trignometric equation 4cos^2theta+6sin^2theta=5 prove tha...

    Text Solution

    |

  3. Consider the equation sintheta+sin3theta+sin5theta=0 prove that sin3th...

    Text Solution

    |

  4. Consider the equation sintheta+sin3theta+sin5theta=0 prove that the ge...

    Text Solution

    |

  5. Consider the equation costheta+sintheta=sqrt2 prove that sin((pi/4)+...

    Text Solution

    |

  6. Consider the equation costheta+sintheta=sqrt2 prove that general sol...

    Text Solution

    |

  7. Consider the equation sqrt3sinx-cosx=sqrt2 prove that sin (x-(pi/6)...

    Text Solution

    |

  8. Consider the equation sqrt3sinx-cosx=sqrt2 Prove that the general so...

    Text Solution

    |

  9. Consider the equation tantheta+sectheta=sqrt3 prove that tan((pi/4)...

    Text Solution

    |

  10. Consider the equation tantheta+sectheta=sqrt3 prove that the general...

    Text Solution

    |

  11. Prove that 2cos(pi/13)cos((9pi)/13)+cos((3pi)/13)+cos((5pi)/13)=0

    Text Solution

    |

  12. Prove that (sin3x+sinx)sinx+(cos3x-cosx)cosx=0

    Text Solution

    |

  13. Prove that (cosx+cosy)^2+(sinx-siny)^2=4cos^2((x+y)/2)

    Text Solution

    |

  14. Prove that (cosA-cosB)^2+(sinA-sinB)^2=4sin^2((A-B)/2)

    Text Solution

    |

  15. Prove that sinx+sin3x+sin5x+sin7x=4cosxcos2xsin4x

    Text Solution

    |

  16. Prove that ((sin7x+sin5x)+(sin9x+sin3x))/((cos7x+cos5x)+(cos9x+cos3x))...

    Text Solution

    |

  17. Prove that sin3x+sin2x-sinx=4sinxcos(x/2)cos((3x)/2)

    Text Solution

    |

  18. Find sin(x/2) , cos(x/2) , and tan(x/2) if tanx=-4/3 and x is in the s...

    Text Solution

    |

  19. Find sin(x/2) , cos(x/2) and tan(x/2) if cosx=(-1/3) and x lies in the...

    Text Solution

    |

  20. Find sin(x/2), cos(x/2) and tan(x/2) if sinx=1/4 and x lies in the sec...

    Text Solution

    |