Precalculus

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Doing some test corrections and not seeing this....Please help:

Verify.

csc^4x - cot^4x = 2csc^2x-1

  • Precalculus -

    Not a surprise that you don't get it,
    the two expressions are not equivalent!

    Start from left:
    csc^4(x)-cot^4(x)
    Factor sin^4(x) as denominator:
    =(1-cos^4(x))/sin^4(x)
    Factor as difference of two squares
    = (1 + cos²(x)) (1 - cos²(x)) / sin^4(x)
    =(1 + cos²(x))sin²(x)/sin^4(x)
    =(1+cos²(x))/sin²(x)
    =(2cos²(x)+sin²(x))/sin²(x)
    =2cos²(x)/sin²(x)+1
    =2cot²(x)+1
    (and not 2csc²(x)+1)

  • Precalculus -

    1-csc^4x=2 csc ^2x-csc^4x

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