What is factor sec^4(x)-tan^4(x) ?

The solution to factor sec^4(x)-tan^4(x) is (sec^2(x)+tan^2(x))(sec(x)+tan(x))(sec(x)-tan(x))

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factor sec^4(x)-tan^4(x)

factor

sec^{4} (x) - tan^{4} (x)

(sec^{2} (x) + tan^{2} (x)) (sec (x) + tan (x)) (sec (x) - tan (x))

Solution steps

sec^{4} (x) - tan^{4} (x)

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

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

= (sec^{2} (x))^{2} - (tan^{2} (x))^{2}

Apply Difference of Two Squares Formula:

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

(sec^{2} (x))^{2} - (tan^{2} (x))^{2} = (sec^{2} (x) + tan^{2} (x)) (sec^{2} (x) - tan^{2} (x))

= (sec^{2} (x) + tan^{2} (x)) (sec^{2} (x) - tan^{2} (x))

Factor

sec^{2} (x) - tan^{2} (x) : (sec (x) + tan (x)) (sec (x) - tan (x))

= (sec^{2} (x) + tan^{2} (x)) (sec (x) + tan (x)) (sec (x) - tan (x))

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

1 - 2 sin^{2} (x)

\frac{sec ^{2} ( x ) - 1}{sec ^{2} ( x )}

\frac{4}{5 + 1} + 1

9 + 220 - 21 + 280

What is factor sec^4(x)-tan^4(x) ?
The solution to factor sec^4(x)-tan^4(x) is (sec^2(x)+tan^2(x))(sec(x)+tan(x))(sec(x)-tan(x))