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Math Help - identities

  1. #1
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    identities

    Hi Guys would be grateful for some help on this question

    Find in exact form, all roots of the equation 2sinx + cosecx = 3 which lies between 0 and 360 degrees.

    thankyou
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  2. #2
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    Quote Originally Posted by gracey View Post
    Hi Guys would be grateful for some help on this question

    Find in exact form, all roots of the equation 2sinx + cosecx = 3 which lies between 0 and 360 degrees.

    thankyou
    First replace sin x with w, say. Then you have 2 w^2 + 1/w^2 = 3 => 2w^4 + 1 = 3w^2 => 2w^4 - 3w^2 + 1 = 0 => (2w^2 - 1)(w^2 - 1) = 0.

    Solve for w (four solutions). Use those values to solve the four different equations sin x = w (one equation for each value of w) ....
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