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Algebra II Part 2

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Verify the identity cot{0-pi/2=-tan 0

  • Algebra II Part 2 - ,

    use the identities:
    tan(x)=sin(x)/cos(x)
    cot(x)=cos(x)/sin(x)
    and
    sin(π/2)=1, cos(π/2)=0
    sin(0)=0, cos(0)=1

  • Algebra II Part 2 - ,

    I think she means θ when using 0
    I'll use x to avoid copy/paste of special characters.

    one way:
    recall the definition of co-functions: function of complementary angle. So,

    cos(x) = sin(pi/2 - x)
    cot(x) = tan(pi/2 -x)

    so, cot(x-pi/2) = -cot(pi/2 - x) = -tan(x)

    or, use cot addition formula:

    cot(x-pi/2) = (1+cotx cot pi/2)/(cot pi/2 - cot x) = (1+0)/(0-cotx) = 1/-cotx = -tanx

  • Algebra II Part 2 - ,

    Thanks Steve, good thought!

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