展开 tan^2(x)-sin^2(x)(cot^2(x)+tan(x))^2

解答

展开

tan^{2} (x) - sin^{2} (x) (cot^{2} (x) + tan (x))^{2}

tan^{2} (x) - sin^{2} (x) cot^{4} (x) - 2 sin^{2} (x) cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

求解步骤

tan^{2} (x) - sin^{2} (x) (cot^{2} (x) + tan (x))^{2}

展开

(cot^{2} (x) + tan (x))^{2} : cot^{4} (x) + 2 cot^{2} (x) tan (x) + tan^{2} (x)

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

使用分配律:

m (a + b + c) = ma + mb + m c

- sin^{2} (x) (cot^{4} (x) + 2 cot^{2} (x) tan (x) + tan^{2} (x)) = - sin^{2} (x) cot^{4} (x) - sin^{2} (x) \cdot 2 cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

= tan^{2} (x) - sin^{2} (x) cot^{4} (x) - sin^{2} (x) \cdot 2 cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

= tan^{2} (x) - sin^{2} (x) cot^{4} (x) - 2 sin^{2} (x) cot^{2} (x) tan (x) - sin^{2} (x) tan^{2} (x)

e x p an d \frac{2 x ( x + 1 ) ( x - 1 )}{x ^{4} + 6 x ^{2} + 1}

e x p an d \frac{7}{( x - 1 ) ( x + 2 )}

e x p an d 5 y^{3} d x - y^{2} (- 2 x + y^{2} x^{4}) d y

e x p an d (3 + 3 cos (x))^{2}

e x p an d e^{t} (1 + e^{2})