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

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

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

simplify

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

sin (2 x) - 1

Solution steps

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

Simplify

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

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

Apply rule:

a (- b) = - ab

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

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

Apply exponent rule:

aa = a^{2}

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

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

Simplify

(sin (x) - cos (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

(3 x - 3)^{4}

\frac{0.1 ( s + 1 ) ( s + 30.1 )}{s}

\frac{( x + 1 ) ^{2}}{2}

(\frac{3}{2}, \frac{5}{4}) y (\frac{1}{2}, - \frac{3}{4})

\frac{x - 1}{x ^{2} ( x - 2 ) ^{3}}

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