What is (cos(x)-sin(x))(sin(x)-cos(x)) ?

The solution to (cos(x)-sin(x))(sin(x)-cos(x)) is sin(2x)-1

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

simplify

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

sin (2 x) - 1

Solution steps

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

Simplify

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

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

Apply rule:

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))

Apply exponent rule:

aa = a^{2}

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

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

Simplify

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

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

Apply the distributive law:

- (- a + b) = a - b

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

= sin (2 x) - 1

y ln (y) d x + (x + y) d y

(4 - 2 i)^{5}

sin (x) (1 - sin (x))

\frac{e ^{- 7 s}}{( s - 3 ) ( s - 1 )}

x (5 - x)

What is (cos(x)-sin(x))(sin(x)-cos(x)) ?
The solution to (cos(x)-sin(x))(sin(x)-cos(x)) is sin(2x)-1