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

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

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

factor

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

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

Solution steps

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

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Factor

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

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

\frac{4}{3} (2)

\frac{1}{7} \cdot \frac{5}{2}

\frac{24 x ^{2} + 4 x}{4 x}

x^{6} - x^{3}

3051 (3)^{6}

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