展开 (tan(x)-1)(sec(x)tan(x))

解答

展开

(tan (x) - 1) (sec (x) tan (x))

tan^{2} (x) sec (x) - sec (x) tan (x)

求解步骤

(tan (x) - 1) (sec (x) tan (x))

= (sec (x) tan (x)) (tan (x) - 1)

使用分配律:

a (b - c) = ab - a c

(sec (x) tan (x)) (tan (x) - 1) = sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

= sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1

化简

sec (x) tan (x) tan (x) - sec (x) tan (x) \cdot 1 : tan^{2} (x) sec (x) - sec (x) tan (x)

= tan^{2} (x) sec (x) - sec (x) tan (x)

e x p an d \frac{5832 x ( - 9 x ^{2} + 1 )}{( 1 + 9 x ^{2} ) ^{4}}

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

e x p an d (sin (x) + 3) (sin (x) - 4)

e x p an d 2 (4 - π)

e x p an d \frac{6 ( 4 x ^{6} - 6 x ^{3} + 4 x ^{2} - 5 x + 6 )}{( 3 x - 1 )}