化简 (10+tan(x))(10-tan(x))+sec^2(x)

解答

化简

(10 + tan (x)) (10 - tan (x)) + sec^{2} (x)

101

求解步骤

(10 + tan (x)) (10 - tan (x)) + sec^{2} (x)

展开

(10 + tan (x)) (10 - tan (x)) : 100 - tan^{2} (x)

= 100 - tan^{2} (x) + sec^{2} (x)

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

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

= 100 + 1

数字相加:

100 + 1 = 101

= 101

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