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

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

Popular >

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

expand

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

- sin (x) + 1

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= - sin (x) + 1

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

x^{2} - (23 + 1) x + 23

\frac{1}{( x - 5 ) ^{4}}

\frac{s}{( s ^{2} + 4 ) ( s ^{2} + 9 )}

x^{4} e^{x} - 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

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