展开 2sec(pi/4 (x+3))

解答

展开

2 sec (\frac{π}{4} (x + 3))

- \frac{2 2}{cos ( \frac{π x}{4} ) + sin ( \frac{π x}{4} )}

求解步骤

2 sec (\frac{π}{4} (x + 3))

乘开

\frac{π}{4} (x + 3) : \frac{π}{4} x + 3 \cdot \frac{π}{4}

= 2 sec (\frac{π}{4} x + 3 \cdot \frac{π}{4})

使用三角恒等式改写

= 2 (- \frac{2}{cos ( \frac{π x}{4} ) + sin ( \frac{π x}{4} )})

化简

2 (- \frac{2}{cos ( \frac{π x}{4} ) + sin ( \frac{π x}{4} )}) : - \frac{2 2}{cos ( \frac{π x}{4} ) + sin ( \frac{π x}{4} )}

= - \frac{2 2}{cos ( \frac{π x}{4} ) + sin ( \frac{π x}{4} )}

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

e x p an d \frac{5}{( x - 2 ) ( x + 3 )}

e x p an d \frac{8 x}{( x ^{2} + 1 ) ^{2}}

e x p an d \frac{( x - 5 ) ( x + 4 )}{x ^{2} + x + 30}

e x p an d \frac{d x}{x ( x ^{2} + 5 )}