展开 4(3cos(t)+1)-(3sin(t)+3)^2sin(3cos(t)+1)

解答

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4 (3 cos (t) + 1) - (3 sin (t) + 3)^{2} sin (3 cos (t) + 1)

12 cos (t) + 4 - 9 sin^{2} (t) sin (3 cos (t) + 1) - 18 sin (3 cos (t) + 1) sin (t) - 9 sin (3 cos (t) + 1)

求解步骤

4 (3 cos (t) + 1) - (3 sin (t) + 3)^{2} sin (3 cos (t) + 1)

= 4 (3 cos (t) + 1) - sin (3 cos (t) + 1) (3 sin (t) + 3)^{2}

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4 (3 cos (t) + 1) : 12 cos (t) + 4

= 12 cos (t) + 4 - sin (3 cos (t) + 1) (3 sin (t) + 3)^{2}

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- sin (3 cos (t) + 1) (3 sin (t) + 3)^{2} : - 9 sin^{2} (t) sin (3 cos (t) + 1) - 18 sin (3 cos (t) + 1) sin (t) - 9 sin (3 cos (t) + 1)

= 12 cos (t) + 4 - 9 sin^{2} (t) sin (3 cos (t) + 1) - 18 sin (3 cos (t) + 1) sin (t) - 9 sin (3 cos (t) + 1)

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

e x p an d (2 \times (- 5) γ)^{3}

s im pl i f y y \cdot 6 sin (3 x - 2 y) (x + 3 y)^{2} + x \cdot (- 9) sin (3 x - 2 y)

e x p an d C_{4} (- 27 e^{- 3 x} x + 27 e^{- 3 x})

s im pl i f y - \frac{2 x}{( x ^{2} + 1 ) ^{2}} + 5 x^{4} cos (x) - x^{5} sin (x)