expand (4(sin(2pin)-2pincos(2pin)))/(pi^2n^2)

פתרון

expand

\frac{4 ( sin ( 2 πn ) - 2 πn cos ( 2 πn ) )}{π ^{2} n ^{2}}

\frac{4 sin ( 2 πn )}{π ^{2} n ^{2}} - \frac{8 cos ( 2 πn )}{πn}

צעדי פתרון

\frac{4 ( sin ( 2 πn ) - 2 πn cos ( 2 πn ) )}{π ^{2} n ^{2}}

4 (sin (2 πn) - 2 πn cos (2 πn))

הרחב את:

4 sin (2 πn) - 8 πn cos (2 πn)

= \frac{4 sin ( 2 πn ) - 8 πn cos ( 2 πn )}{π ^{2} n ^{2}}

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

: השתמש בתכונת השברים הבאה

\frac{4 sin ( 2 πn ) - 8 πn cos ( 2 πn )}{π ^{2} n ^{2}} = \frac{4 sin ( 2 πn )}{π ^{2} n ^{2}} - \frac{8 πn cos ( 2 πn )}{π ^{2} n ^{2}}

= \frac{4 sin ( 2 πn )}{π ^{2} n ^{2}} - \frac{8 πn cos ( 2 πn )}{π ^{2} n ^{2}}

\frac{8 πn cos ( 2 πn )}{π ^{2} n ^{2}}

צמצם את:

\frac{8 cos ( 2 πn )}{πn}

= \frac{4 sin ( 2 πn )}{π ^{2} n ^{2}} - \frac{8 cos ( 2 πn )}{πn}

s im pl i f y (3 x + 22)^{2}

e x p an d (cot (a) + sec (a)) csc (a)

e x p an d (e^{x} + e^{x} x) (e^{x})

e x p an d [cos (7 t) (5 + sinh (\frac{3 t}{2}) + e^{2 t})]

\frac{d}{d x} ((e^{x}) (5 e^{5 x} - 25 x))