What is expand (tan^2(12x)-cot^2(12x))^2 ?

The solution to expand (tan^2(12x)-cot^2(12x))^2 is tan^4(12x)-2tan^2(12x)cot^2(12x)+cot^4(12x)

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expand (tan^2(12x)-cot^2(12x))^2

expand

(tan^{2} (12 x) - cot^{2} (12 x))^{2}

tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

Solution steps

(tan^{2} (12 x) - cot^{2} (12 x))^{2}

Apply Perfect Square Formula:

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

(tan^{2} (12 x) - cot^{2} (12 x))^{2} = (tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2}

= (tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2}

Simplify

(tan^{2} (12 x))^{2} - 2 tan^{2} (12 x) cot^{2} (12 x) + (cot^{2} (12 x))^{2} : tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

= tan^{4} (12 x) - 2 tan^{2} (12 x) cot^{2} (12 x) + cot^{4} (12 x)

(e^{y} - e^{- y})^{2}

43 (35 + 2)

2 y d y - (3 y^{2} cot (x) - sin (x) cos (x)) d x

(\frac{x}{9} + 1)^{4}

(16 x y - 3 x^{2}) d x + (8 x^{2} + 2 y) d y

What is expand (tan^2(12x)-cot^2(12x))^2 ?
The solution to expand (tan^2(12x)-cot^2(12x))^2 is tan^4(12x)-2tan^2(12x)cot^2(12x)+cot^4(12x)