Posted by Joseph on Thursday, December 9, 2010 at 6:45pm.
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)
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