展开 (tan(pi(x+2)))/(x+2)

解答

展开

\frac{tan ( π ( x + 2 ) )}{x + 2}

\frac{tan ( π x )}{x + 2}

求解步骤

\frac{tan ( π ( x + 2 ) )}{x + 2}

乘开

π (x + 2) : π x + 2 π

= \frac{tan ( π x + 2 π )}{x + 2}

使用三角恒等式改写

= \frac{\frac{s i n ( π x )}{c o s ( π x )}}{x + 2}

使用分式法则:

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

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

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

= \frac{tan ( π x )}{( x + 2 )}

去除括号:

(a) = a

= \frac{tan ( π x )}{x + 2}

e x p an d 1 - (x + 1) e^{- x}

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

e x p an d (3 x - 3) (sin (x) + 1)

e x p an d \frac{( π ( 1 + e ^{(- s)} ) )}{( ( s ^{2} + π ^{2} ) ( s ^{2} + s ) )}

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