展开 (tan^{(2)}(y)-cot^{(2)}(y))^{(2)}

解答

展开

(tan^{(2)} (y) - cot^{(2)} (y))^{(2)}

tan^{4} (y) - 2 tan^{2} (y) cot^{2} (y) + cot^{4} (y)

求解步骤

(tan^{2} (y) - cot^{2} (y))^{2}

使用完全平方公式:

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

(tan^{2} (y) - cot^{2} (y))^{2} = (tan^{2} (y))^{2} - 2 tan^{2} (y) cot^{2} (y) + (cot^{2} (y))^{2}

= (tan^{2} (y))^{2} - 2 tan^{2} (y) cot^{2} (y) + (cot^{2} (y))^{2}

化简

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

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

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