簡約 (cos(x)-sin(x))*(sin(x)-cos(x))

解

簡約

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

sin (2 x) - 1

解答ステップ

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

簡素化

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

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

規則を適用する:

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))

指数の規則を適用する:

aa = a^{2}

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

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

簡素化

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

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

分配法則を適用する:

- (- a + b) = a - b

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

= sin (2 x) - 1