What is factor csc^4(x)-cot^4(x) ?

The solution to factor csc^4(x)-cot^4(x) is (csc^2(x)+cot^2(x))(csc(x)+cot(x))(csc(x)-cot(x))

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factor csc^4(x)-cot^4(x)

factor

csc^{4} (x) - cot^{4} (x)

(csc^{2} (x) + cot^{2} (x)) (csc (x) + cot (x)) (csc (x) - cot (x))

Solution steps

csc^{4} (x) - cot^{4} (x)

csc^{4} (x) = (csc^{2} (x))^{2}

cot^{4} (x) = (cot^{2} (x))^{2}

= (csc^{2} (x))^{2} - (cot^{2} (x))^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(csc^{2} (x))^{2} - (cot^{2} (x))^{2} = (csc^{2} (x) + cot^{2} (x)) (csc^{2} (x) - cot^{2} (x))

= (csc^{2} (x) + cot^{2} (x)) (csc^{2} (x) - cot^{2} (x))

Factor

csc^{2} (x) - cot^{2} (x) : (csc (x) + cot (x)) (csc (x) - cot (x))

= (csc^{2} (x) + cot^{2} (x)) (csc (x) + cot (x)) (csc (x) - cot (x))

(1 + 2 x^{3})^{5}

(x + 4) (x - 2) + (x - 6) (x + 4) - 2 x^{2}

\frac{1}{x - 4} - \frac{5}{( x - 4 ) ^{3}} - \frac{2}{( x - 4 ) ^{2}}

(1 + i) (2 - i)

(2 n - 1)^{3}

What is factor csc^4(x)-cot^4(x) ?
The solution to factor csc^4(x)-cot^4(x) is (csc^2(x)+cot^2(x))(csc(x)+cot(x))(csc(x)-cot(x))