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March 6, 2015

March 6, 2015

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

Verify.

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

- Precalculus -
**MathMate**, Friday, December 10, 2010 at 8:43amNot 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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