What is expand (sec^2(x)-1)^2 ?

The solution to expand (sec^2(x)-1)^2 is tan^4(x)

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expand (sec^2(x)-1)^2

expand

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

tan^{4} (x)

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(sec^{2} (x) - 1)^{2} = (sec^{2} (x))^{2} - 2 sec^{2} (x) \cdot 1 + 1^{2}

= (sec^{2} (x))^{2} - 2 sec^{2} (x) \cdot 1 + 1^{2}

Simplify

(sec^{2} (x))^{2} - 2 sec^{2} (x) \cdot 1 + 1^{2} : tan^{4} (x)

= tan^{4} (x)

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(4 x^{3} e^{x}) (x^{2} + 1)

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

2 (sin (t)) (t) (7 - t^{2})

(2 t^{3} + 3 y) d t

What is expand (sec^2(x)-1)^2 ?
The solution to expand (sec^2(x)-1)^2 is tan^4(x)