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

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

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

expand

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

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

Solution steps

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

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})

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

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

y (x + y + 1) d x + x (x + 3 y + 2) d y

\frac{9 x ^{2} - 8}{( x - 3 ) ( 2 x - 5 )}

(x - 5) (x + 7)

(x + Δ x)^{5}

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