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23 November, 11:24

2. Solve the following equations for 0° Sx < 180°.

(i) cosec (x+10°) = 3

(ii) cot (x - 30°) = 0.45.

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  1. 23 November, 11:42
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    See below in bold.

    Step-by-step explanation:

    (1) cosec (x + 10) = 3

    Now cosec x = 1/sin x so

    1 / sin (x + 10) = 3

    3 sin (x + 10) = 1

    sin (x + 10) = 1/3

    x + 10 = 19.47, 160.53 degrees

    x = 9.47, 150.53 degrees.

    (ii) cot (x - 30) = 0.45

    cot (x - 30) = 1 / tan (x - 30) so we have

    tan (x - 30) = 1 / 0.45 = 2.2222

    x - 30 = 65.77 degrees

    x = 95.77 degrees.
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