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State the restrictions on the variables for these trigonometric identities.
a)(1 + 2 sin x cos x)/ (sin x + cos x) = sin x + cos x
b) sin x /(1+ cos x) = csc x - cot x

  • Math -

    generally, restrictions on variables are caused by denominators being zero
    so in #1
    sinx + cosx = 0 causes problems
    sinx = -cosx
    sinx/cosx = -1
    tanx = -1 , x is in quadrants II or IV
    x = 135 or 225 degrees
    or 3pi/4 or 5pi/4 radians

    #2.
    first of all on the right side we have
    cscx and cotx
    sinxe cscx = 1/sinx, and cotx = cosx/sinx , whenever the sinx = 0 we have an undefined value
    sinx = 0 for x = 0, 180 , and 360 degrees or 0, pi, 2pi radians

    secondly we have to worry about 1+cosx
    1 + cosx = 0
    cosx = -1
    x = 180 degrees or pi radians

    so the restrictions are 0, pi, 2pi radians, or
    0, 180 and 360 degrees

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