化简 (e^{ti}+e^{-ti})^3

解答

化简

(e^{t i} + e^{- t i})^{3}

8 cos^{3} (t)

求解步骤

(e^{t i} + e^{- t i})^{3}

e^{t i} = cos (t) + i sin (t)

e^{- t i} = cos (t) - i sin (t)

= (cos (t) + i sin (t) + cos (t) - i sin (t))^{3}

化简

cos (t) + sin (t) i + cos (t) - i sin (t) : 2 cos (t)

= (2 cos (t))^{3}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{3} cos^{3} (t)

2^{3} = 8

= 8 cos^{3} (t)

e x p an d (n^{2} + n + 5)^{10}

e x p an d f_{x} (1, - 2)

e x p an d 3 sin (5 (x - 7)) + 7

e x p an d - \frac{\frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

e x p an d \frac{- 4 s ^{2} - 16 s - 15}{( 2 s - 1 ) ( s + 2 ) ^{3}}