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Solving Equations Using Trigonometric Identities

  1. Nov 10, 2012 #1
    Hey PF!

    1. The problem statement, all variables and given/known data
    Find exact solutions for the following equations over the domain 0 ≤ x <2π
    2sinx = 3 + 2cscx

    2. Relevant equations

    3. The attempt at a solution
    2sinx = 3 + 2cscx
    2sinx = 3 +2(1/sinx)
    sinx = 3/2 + 1/sinx
    sinx - 1/sinx = 3/2
    (1-1-cos2x)/sinx = 3/2
    -cos2x/sinx = 3/2
    cos2x/sinx = -3/2

    I am perplexed by this question. Where do I go from here? How do I solve this equation?
  2. jcsd
  3. Nov 10, 2012 #2


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    No need to change sin2(x) into 1-cos2(x) .

    Multiply both sides of sin(x) = 3/2 + 1/sin(x) by sin(x) .
  4. Nov 10, 2012 #3
    Ahhhh... Thank you for elucidating me. I can see now that I have to factor and solve for x. Thank you again for your help!
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