promotion image of download ymail app
Promoted

Prove: (SinX+Sin2X+ Sin3X+ Sin4X+ Sin5X)/ (CosX+ Cos2X+ Cos3X+ Cos4X+ Cos5X)=tan3X?

Can anyone prove: (SinX+Sin2X+ Sin3X+ Sin4X+ Sin5X)/ (CosX+ Cos2X+ Cos3X+ Cos4X+ Cos5X)=tan3X

1 Answer

Relevance
  • Ben
    Lv 7
    8 years ago
    Favorite Answer

    Start with:

    (SinX+Sin2X+ Sin3X+ Sin4X+ Sin5X)/ (CosX+ Cos2X+ Cos3X+ Cos4X+ Cos5X)

    Rewrite this as follows:

    (Sin(3x - 2x)+Sin(3x-x)+ Sin(3x)+ Sin(3x+x)+ Sin(3x+2x))/ (Cos(3x-2x)+ Cos(3x-x)+ Cos3X+ Cos(3x+x)+ Cos(3x+2x))

    Now, use the sum to product formula, then factor to get

    {sin(3x)[1 + 2cosx + 2cos(2x)] + 0*cos(3x)}/{cos(3x)[1 + 2cosx + 2cos(2x)] + 0*sin(3x)} =

    sin(3x)/cos(3x) =

    tan(3x)

    QED

    Remember: sin(-x) = -sin(x); cos(-x) = cos(x)

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.