化简 (cos(x)-sin(x))(sin(x)-cos(x))

解答

化简

(cos (x) - sin (x)) (sin (x) - cos (x))

sin (2 x) - 1

求解步骤

(cos (x) - sin (x)) (sin (x) - cos (x))

化简

sin (x) - cos (x) : - (cos (x) - sin (x))

= (cos (x) - sin (x)) (- (cos (x) - sin (x)))

使用法则:

a (- b) = - ab

(cos (x) - sin (x)) (- (cos (x) - sin (x))) = - (cos (x) - sin (x)) (cos (x) - sin (x))

= - (cos (x) - sin (x)) (cos (x) - sin (x))

使用指数法则:

aa = a^{2}

- (cos (x) - sin (x)) (cos (x) - sin (x)) = - (cos (x) - sin (x))^{2}

= - (cos (x) - sin (x))^{2}

化简

(cos (x) - sin (x))^{2} : - sin (2 x) + 1

= - (- sin (2 x) + 1)

使用分配律:

- (- a + b) = a - b

- (- sin (2 x) + 1) = sin (2 x) - 1

= sin (2 x) - 1

e x p an d y ln (y) d x + (x + y) d y

s im pl i f y (4 - 2 i)^{5}

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

e x p an d \frac{e ^{- 7 s}}{( s - 3 ) ( s - 1 )}

s im pl i f y x (5 - x)