What is expand sin(x/2)(2sin(x/2)-1) ?

The solution to expand sin(x/2)(2sin(x/2)-1) is 2sin^2(x/2)-sin(x/2)

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expand sin(x/2)(2sin(x/2)-1)

expand

sin (\frac{x}{2}) (2 sin (\frac{x}{2}) - 1)

2 sin^{2} (\frac{x}{2}) - sin (\frac{x}{2})

Solution steps

sin (\frac{x}{2}) (2 sin (\frac{x}{2}) - 1)

Apply the distributive law:

a (b - c) = ab - a c

sin (\frac{x}{2}) (2 sin (\frac{x}{2}) - 1) = sin (\frac{x}{2}) \cdot 2 sin (\frac{x}{2}) - sin (\frac{x}{2}) \cdot 1

= sin (\frac{x}{2}) \cdot 2 sin (\frac{x}{2}) - sin (\frac{x}{2}) \cdot 1

sin (\frac{x}{2}) \cdot 2 sin (\frac{x}{2}) = 2 sin^{2} (\frac{x}{2})

sin (\frac{x}{2}) \cdot 1 = sin (\frac{x}{2})

= 2 sin^{2} (\frac{x}{2}) - sin (\frac{x}{2})

(y + 1) e^{x}

(2 x + \frac{1}{3 x})^{18}

x^{2} (ln (x + 2) - 1) d x

\frac{4}{x ( x + 2 )}

(x - 8 - 5) (x - 8 + 5)

What is expand sin(x/2)(2sin(x/2)-1) ?
The solution to expand sin(x/2)(2sin(x/2)-1) is 2sin^2(x/2)-sin(x/2)