化简 (11+cot(x))(11-cot(x))+csc^2(x)

解答

化简

(11 + cot (x)) (11 - cot (x)) + csc^{2} (x)

122

求解步骤

(11 + cot (x)) (11 - cot (x)) + csc^{2} (x)

展开

(11 + cot (x)) (11 - cot (x)) : 121 - cot^{2} (x)

= 121 - cot^{2} (x) + csc^{2} (x)

使用毕达哥拉斯恒等式:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - cot^{2} (x) = 1

= 121 + 1

数字相加:

121 + 1 = 122

= 122

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