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Math Methods problem (Trig question)

  1. Apr 13, 2004 #1
    I have 2 problems. First, solve 2cosX + tanX = secX where X is greater than or equal to zero and less than 2 pi. I understand that the secant is basically the inverse of the cosine, (hyp/adj), but I have no idea how to solve for this. I also don't understand how to solve an equation with 2 different trig functions in it (sin and cos)
    Please help!

    Also, it says solve 2sinX + cotX = cscX where X is defined by the same parameters as mentioned above. I have the same problem. Help! Thanks!!!!!!
     
  2. jcsd
  3. Apr 14, 2004 #2

    arildno

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    A few hints:
    1. Multiply your equation with cos(x).
    2. Use a well-known identity to exress cos^(2)(x) in terms of sin(x)
    3. Solve for sin(x)
     
  4. Apr 14, 2004 #3
    Basically arilno's ideas:

    2cos(x) + tan(x) = 1/cos (x)

    2cos^2 (x) + cos(x) (sin(x) / cos(x)) = 1

    The well known identities: cos^2(x) + sin^2 (x) = 1, tan(x) = sin(x) / cos(x).

    2 (1 - sin^2 (x)) + sin(x) = 1

    2 - 2sin^2 (x) + sin(x) = 1

    2sin^2 (x) - sin(x) - 1 = 0

    This is a quadratic equation.

    (2 sin(x) + 1)*(sin(x) - 1) = 0

    sin(x) = -1/2 or sin(x) = 1
     
  5. Apr 15, 2004 #4
    sinx =1 is not applicable coz it is not in the domain
     
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