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21 July, 11:11

Solve Tan^2x/2-2 cos x = 1 for 0 < or equal to theta < greater or equal to 1.

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  1. 21 July, 14:05
    0
    x = theta = 0°

    Step-by-step explanation:

    Given the trigonometry function

    Tan²x/2-2 cos x = 1

    Tan²x-4cosx = 2 ... 1

    From trigonometry identity

    Sec²x = tan²x+1

    tan²x = sec²x-1 ... 2

    Substituting 2 into 1, we have:

    sec²x-1 - 4cosx = 2

    Note that secx = 1/cosx

    1/cos²x - 1 - 4cosx = 2

    Let cosx. = P

    1/P² - 1 - 4P = 2

    1-P²-4P³ = 2P²

    4P³+2P²+P²-1 = 0

    4P³+3P² = 1

    P² (4P+3) = 1

    P² = 1 and 4P+3 = 1

    P = ±1 and P = - 3/4

    Since cosx = P

    If P = 1

    Cosx = 1

    x = arccos1

    x = 0°

    If x = - 1

    cosx = - 1

    x = arccos (-1)

    x = 180°

    Since our angle must be between 0 and 1 therefore x = 0°
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