化简 (12+tan(x))(12-tan(x))+sec^2(x)

解答

化简

(12 + tan (x)) (12 - tan (x)) + sec^{2} (x)

145

求解步骤

(12 + tan (x)) (12 - tan (x)) + sec^{2} (x)

展开

(12 + tan (x)) (12 - tan (x)) : 144 - tan^{2} (x)

= 144 - 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

= 144 + 1

数字相加:

144 + 1 = 145

= 145

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