What is expand (sin(x/2)+cos(x/2))^2-sin(x) ?

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

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expand (sin(x/2)+cos(x/2))^2-sin(x)

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(sin (\frac{x}{2}) + cos (\frac{x}{2}))^{2} = sin^{2} (\frac{x}{2}) + 2 sin (\frac{x}{2}) cos (\frac{x}{2}) + cos^{2} (\frac{x}{2})

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

Simplify

sin^{2} (\frac{x}{2}) + 2 sin (\frac{x}{2}) cos (\frac{x}{2}) + cos^{2} (\frac{x}{2}) : sin (2 \cdot \frac{x}{2}) + 1

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

(x + 3 - 23) (x + 3 + 23)

(z - \frac{1}{2}) (z - \frac{1}{5})

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

\frac{25}{( t + 1 ) ^{2}}

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

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