展开 (1+csc(a))(1csc(a)=-cot^2(a))

解答

展开

(1 + csc (a)) (1 csc (a) = - cot^{2} (a))

csc (a) = - csc (a) cot^{2} (a)

求解步骤

(1 + csc (a)) (1 \cdot csc (a) = - cot^{2} (a))

= (1 + csc (a)) (1 = csc (a) - cot^{2} (a))

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = csc (a), c = 1 \cdot csc (a) =, d = - cot^{2} (a)

1 \cdot 1 \cdot csc (a) = 1 \cdot (- cot^{2} (a)) + csc (a) \cdot 1 \cdot csc (a) = csc (a) (- cot^{2} (a))

使用加减运算法则

+ (- a) = - a

1 \cdot 1 \cdot csc (a) = - 1 \cdot cot^{2} (a) + 1 \cdot csc (a) csc (a) = - csc (a) cot^{2} (a)

乘开

1 \cdot 1 \cdot csc (a) : csc (a)

csc (a) = - csc (a) cot^{2} (a)

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