Results 1 to 3 of 3

Math Help - trigonometric equation

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    66

    Unhappy trigonometric equation

    1. Prove that the equation is true.
    cos55*+cos65*+cos175*=0
    2. Solve the equation:
    sin4x+sin2x=sinx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615
    Hello, blertta!

    Prove: . \cos55^o+\cos65^o+\cos175^o \:=\:0
    Sum-to-product identity: . \cos A + \cos B \:=\:2\cdot\cos\left(\frac{A+B}{2}\right)\cos\left  (\frac{A-B}{2}\right)


    \text{We have: }\;\cos55^o + \underbrace{\cos65^o + \cos175^o}

    . . . . . = \;\cos55^o + \overbrace{2\cdot\cos120^o\cos55^o}

    . . . . . = \;\cos55^o + 2\left(-\frac{1}{2}\right)\cos55^o

    . . . . . = \;\cos55^o - \cos55^o

    . . . . . =\qquad\quad0

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2007
    Posts
    329
    \sin (4x)+\sin (2x)=2\cos x\sin x + 4 \cos^3 x \sin x - 4 \cos x  \sin^3 x.
    So if \sin x\ne 0 (You should check \sin x = 0 as it might be a solution!): \cos x \left(1 + 2 \cos^2 x - 2 \sin^2 x\right)=0\iff \cos x\left(1+2\cos 2x\right)=0.
    So if \cos x\ne 0 (You should check \cos x = 0 as well!): \cos 2x=-\frac 12.
    You can finish it from here. I hope I didn't make any mistakes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 27th 2011, 12:26 AM
  2. trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: September 9th 2009, 06:36 AM
  3. trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 22nd 2009, 12:59 AM
  4. Replies: 2
    Last Post: April 28th 2009, 06:42 AM
  5. Trigonometric Equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 5th 2008, 10:19 AM

Search Tags


/mathhelpforum @mathhelpforum