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algebra

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given that sin (2x+30)=cos(x-15).determine the value of x given x is an acute angle

  • algebra -

    assuming that x is in degrees, then knowing that cos(x) = sin(90-x), we have

    sin(2x+30) = sin(90-(x-15))
    sin(2x+30) = sin(105-x)
    so,
    2x+30 = 105-x
    3x = 75
    x = 25

    check:
    sin(80) = cos(10)
    yep.

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