化简 (cos(x)-sin(x))*(sin(x)-cos(x))

解答

化简

(cos (x) - sin (x)) \cdot (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

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

e x p an d cos (x) (tan (x) + sec (x))

s im pl i f y (- 1 + \frac{4 i}{n})^{3}

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