zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

展开 (csc(x)-cot(x))^4

解答

展开

(csc (x) - cot (x))^{4}

解答

csc^{4} (x) - 4 csc^{3} (x) cot (x) + 6 csc^{2} (x) cot^{2} (x) - 4 cot^{3} (x) csc (x) + cot^{4} (x)

求解步骤

(csc (x) - cot (x))^{4}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = csc (x), b = - cot (x)

= i = 0 \sum 4 (i 4) csc^{(4 - i)} (x) (- cot (x))^{i}

展开求和

= \frac{4 !}{0 ! ( 4 - 0 ) !} csc^{4} (x) (- cot (x))^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} csc^{3} (x) (- cot (x))^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} csc^{2} (x) (- cot (x))^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} csc^{1} (x) (- cot (x))^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} csc^{0} (x) (- cot (x))^{4}

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} csc^{4} (x) (- cot (x))^{0} : csc^{4} (x)

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} csc^{3} (x) (- cot (x))^{1} : - 4 csc^{3} (x) cot (x)

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} csc^{2} (x) (- cot (x))^{2} : 6 csc^{2} (x) cot^{2} (x)

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} csc^{1} (x) (- cot (x))^{3} : - 4 cot^{3} (x) csc (x)

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} csc^{0} (x) (- cot (x))^{4} : cot^{4} (x)

= csc^{4} (x) - 4 csc^{3} (x) cot (x) + 6 csc^{2} (x) cot^{2} (x) - 4 cot^{3} (x) csc (x) + cot^{4} (x)

流行的例子

化简 (sqrt(a)+4)^2

s im pl i f y (a + 4)^{2}

化简 (3-sqrt(x+10))*(3+sqrt(x+10))

s im pl i f y (3 - x + 10) \cdot (3 + x + 10)

展开 (1+cos(u))^2

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

展开 ln(x)*(x-ln(x))

e x p an d ln (x) \cdot (x - ln (x))

化简 (asqrt(a)-bsqrt(b))(asqrt(b)+bsqrt(b))

s im pl i f y (a a - b b) (a b + b b)