How do you simplify ${csc}^{4} (x) - {cot}^{4} (x)$ $csc^4(x)-cot^4(x)$ ?

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How do you simplify ${csc}^{4} (x) - {cot}^{4} (x)$ $csc^4(x)-cot^4(x)$ ?

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Answer 1 · 2015-05-21T01:46:30

$f (x) = \frac{1}{{sin}^{4} x} - \frac{{cos}^{4} x}{{sin}^{4} x} = \frac{1 - {cos}^{4} x}{{sin}^{4} x}$ $f(x) = 1/sin^4 x - cos^4x/sin^4 x = (1 - cos^4 x)/sin^4 x$ =

$= \frac{(1 - {cos}^{2} x) (1 + {cos}^{2} x)}{{sin}^{4} x}$ $= [(1 - cos^2 x)(1 + cos^2 x)]/(sin^4 x)$ = $\frac{1 + {cos}^{2} x}{{sin}^{2} x}$ $(1 +cos ^2 x)/sin^2 x$

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How do you simplify ${csc}^{4} (x) - {cot}^{4} (x)$ $csc^4(x)-cot^4(x)$ ?

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How do you simplify csc^4(x)-cot^4(x)csc4(x)−cot4(x)csc^4(x)-cot^4(x)?

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How do you simplify ${csc}^{4} (x) - {cot}^{4} (x)$ $csc^4(x)-cot^4(x)$ ?