расширить (tan^2(12x)-cot^2(12x))^2

Решение

расширить

(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)

Шаги решения

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

Примените формулу полного квадрата:

(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}

Упростите

(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)