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2 October, 16:05

Find value of "x"

Sin (7x-20°) = Cos (3x+40°)

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  1. 2 October, 19:08
    0
    x = 36°n + 7° OR x = 90°n + 37.5° for any integer n

    Step-by-step explanation:

    Since cos (x) = sin (90°-x), we have

    sin (7x-20°) = sin (90° - (3x+40°)) = sin (50° - 3x)

    sin (x) = sin (y) implies either:

    x = 360° n + y

    or

    x = 360°n + 180° - y

    Generally sin (x) = sin (y) ⇒ x = 180°n + (-1) ⁿ y

    First case:

    7x - 20° = 360°n + 50° - 3x

    10x = 360°n + 70°

    x = 36°n + 7°

    Second case:

    7x - 20° = 360°n + 180° - (50°-3x)

    7x - 20° = 360°n + 180° - 50° + 3x

    7x - 20° = 360°n + 130° + 3x

    4x - 20° = 360°n + 130°

    4x = 360°n + 150°

    x = 90°n + 37.5°
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