What is expand-sin(t)θ(t-pi/2) ?

The solution to expand-sin(t)θ(t-pi/2) is -tθsin(t)+(piθsin(t))/2

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expand-sin(t)θ(t-pi/2)

expand

- sin (t) θ (t - \frac{π}{2})

- tθ sin (t) + \frac{π θ sin ( t )}{2}

Solution steps

- sin (t) θ (t - \frac{π}{2})

= - θ sin (t) (t - \frac{π}{2})

Apply the distributive law:

a (b - c) = ab - a c

a = - sin (t) θ, b = t, c = \frac{π}{2}

= - sin (t) θt - (- sin (t) θ) \frac{π}{2}

Apply minus-plus rules

- (- a) = a

= - tθ sin (t) + \frac{π}{2} θ sin (t)

Simplify

- tθ sin (t) + \frac{π}{2} θ sin (t) : - tθ sin (t) + \frac{π θ sin ( t )}{2}

= - tθ sin (t) + \frac{π θ sin ( t )}{2}

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What is expand-sin(t)θ(t-pi/2) ?
The solution to expand-sin(t)θ(t-pi/2) is -tθsin(t)+(piθsin(t))/2