What is expand (cos^2(t)-cos(t)sin(t))*(-sin(t)+cos(t)) ?

The solution to expand (cos^2(t)-cos(t)sin(t))*(-sin(t)+cos(t)) is -cos(t)sin(2t)+cos(t)

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expand (cos^2(t)-cos(t)sin(t))*(-sin(t)+cos(t))

expand

(cos^{2} (t) - cos (t) sin (t)) \cdot (- sin (t) + cos (t))

- cos (t) sin (2 t) + cos (t)

Solution steps

(cos^{2} (t) - cos (t) sin (t)) (- sin (t) + cos (t))

Expand

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

= cos (t) (- sin (2 t) + 1)

Apply the distributive law:

a (b + c) = ab + a c

cos (t) (- sin (2 t) + 1) = cos (t) (- sin (2 t)) + cos (t) \cdot 1

= cos (t) (- sin (2 t)) + cos (t) \cdot 1

Simplify

cos (t) (- sin (2 t)) + cos (t) \cdot 1 : - cos (t) sin (2 t) + cos (t)

= - cos (t) sin (2 t) + cos (t)

\frac{d}{d x} ((1 + x^{2}) arctan (x)) - x

6 y^{2} d x - x (2 x^{3} + y) d y

(6 + x)^{2}

\frac{( k + 1 ) ( k + 2 ) ( k + 3 )}{3}

(cos (x) + i sin (x))^{2}

What is expand (cos^2(t)-cos(t)sin(t))*(-sin(t)+cos(t)) ?
The solution to expand (cos^2(t)-cos(t)sin(t))*(-sin(t)+cos(t)) is -cos(t)sin(2t)+cos(t)