展开 (sec(x)+tan(x))^3

解答

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(sec (x) + tan (x))^{3}

sec^{3} (x) + 3 sec^{2} (x) tan (x) + 3 tan^{2} (x) sec (x) + tan^{3} (x)

求解步骤

(sec (x) + tan (x))^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(sec (x) + tan (x))^{3} = sec^{3} (x) + 3 sec^{2} (x) tan (x) + 3 sec (x) tan^{2} (x) + tan^{3} (x)

= sec^{3} (x) + 3 sec^{2} (x) tan (x) + 3 sec (x) tan^{2} (x) + tan^{3} (x)

= sec^{3} (x) + 3 sec^{2} (x) tan (x) + 3 tan^{2} (x) sec (x) + tan^{3} (x)

e x p an d \frac{n ( 3 + n )}{18}

e x p an d - 4 (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})

e x p an d lo g_{2} (8 x^{(2)} + 80 x + 200)

e x p an d \frac{( s + 2 ) ^{2}}{s ( s + 1 ) ^{3}}

e x p an d 2 (4 x)