展开 (2(-3cos((pin)/3)+3))/(pi^2n^2)

解答

展开

\frac{2 ( - 3 cos ( \frac{πn}{3} ) + 3 )}{π ^{2} n ^{2}}

- \frac{6 cos ( \frac{πn}{3} )}{π ^{2} n ^{2}} + \frac{6}{π ^{2} n ^{2}}

求解步骤

\frac{2 ( - 3 cos ( \frac{πn}{3} ) + 3 )}{π ^{2} n ^{2}}

乘开

2 (- 3 cos (\frac{πn}{3}) + 3) : - 6 cos (\frac{πn}{3}) + 6

= \frac{- 6 cos ( \frac{πn}{3} ) + 6}{π ^{2} n ^{2}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 6 cos ( \frac{πn}{3} ) + 6}{π ^{2} n ^{2}} = - \frac{6 cos ( \frac{πn}{3} )}{π ^{2} n ^{2}} + \frac{6}{π ^{2} n ^{2}}

= - \frac{6 cos ( \frac{πn}{3} )}{π ^{2} n ^{2}} + \frac{6}{π ^{2} n ^{2}}

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