展开 (cos(2pit)-1)(sin(2pit)+1)

解答

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(cos (2 π t) - 1) (sin (2 π t) + 1)

cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

求解步骤

(cos (2 π t) - 1) (sin (2 π t) + 1)

使用 FOIL 方法:

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

a = cos (2 π t), b = - 1, c = sin (2 π t), d = 1

= cos (2 π t) sin (2 π t) + cos (2 π t) \cdot 1 + (- 1) sin (2 π t) + (- 1) \cdot 1

使用加减运算法则

+ (- a) = - a

= cos (2 π t) sin (2 π t) + 1 \cdot cos (2 π t) - 1 \cdot sin (2 π t) - 1 \cdot 1

化简

cos (2 π t) sin (2 π t) + 1 \cdot cos (2 π t) - 1 \cdot sin (2 π t) - 1 \cdot 1 : cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

= cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

e x p an d A (2, - 1, 3) B (1, - 2, - 3)

e x p an d e^{t} (- t e^{- t} - e^{- t})

e x p an d \frac{2 s + 1}{( s ^{2} + 4 s + 3 ) ( s - 2 )}

\frac{d}{d t} ((x) (9 + sin (x)))

e x p an d \frac{2 ( x + h ) + 3}{x + h - 1}