What is expand (cos((2pi)/9)-cos(x))^2+(sin((2pi)/9)-sin(x))^2 ?

The solution to expand (cos((2pi)/9)-cos(x))^2+(sin((2pi)/9)-sin(x))^2 is 2(1-cos((2pi)/9-x))

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expand (cos((2pi)/9)-cos(x))^2+(sin((2pi)/9)-sin(x))^2

expand

(cos (\frac{2 π}{9}) - cos (x))^{2} + (sin (\frac{2 π}{9}) - sin (x))^{2}

2 (1 - cos (\frac{2 π}{9} - x))

Solution steps

(cos (\frac{2 π}{9}) - cos (x))^{2} + (sin (\frac{2 π}{9}) - sin (x))^{2}

(cos (\frac{2 π}{9}) - cos (x))^{2} : cos^{2} (\frac{2 π}{9}) - 2 cos (\frac{2 π}{9}) cos (x) + cos^{2} (x)

= cos^{2} (\frac{2 π}{9}) - 2 cos (\frac{2 π}{9}) cos (x) + cos^{2} (x) + (sin (\frac{2 π}{9}) - sin (x))^{2}

(sin (\frac{2 π}{9}) - sin (x))^{2} : sin^{2} (\frac{2 π}{9}) - 2 sin (\frac{2 π}{9}) sin (x) + sin^{2} (x)

= cos^{2} (\frac{2 π}{9}) - 2 cos (\frac{2 π}{9}) cos (x) + cos^{2} (x) + sin^{2} (\frac{2 π}{9}) - 2 sin (\frac{2 π}{9}) sin (x) + sin^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= - 2 cos (\frac{2 π}{9}) cos (x) - 2 sin (\frac{2 π}{9}) sin (x) + 1 + 1

Add the numbers:

1 + 1 = 2

= - 2 cos (\frac{2 π}{9}) cos (x) - 2 sin (\frac{2 π}{9}) sin (x) + 2

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

- cos (s) cos (t) - sin (s) sin (t) = - cos (s - t)

= 2 (1 - cos (\frac{2 π}{9} - x))

Factor

- 2 cos (\frac{2 π}{9}) cos (x) - 2 sin (\frac{2 π}{9}) sin (x) + 2 : 2 (- cos (\frac{2 π}{9}) cos (x) - sin (\frac{2 π}{9}) sin (x) + 1)

= 2 (- cos (- x + \frac{2 π}{9}) + 1)

(y - \frac{3}{2} x) (y - \frac{1}{2} x) (y - \frac{2}{15} x)

\frac{t ^{4} + 1 ( t - 1 )}{t ( t ^{2} - 2 )}

(2 x - 5 y + 2) d x + (1 - 5 x - 6 y) d y

(x + (\frac{1}{x}))^{8}

(s + 1) (s - 1) (s + \frac{1}{2})

What is expand (cos((2pi)/9)-cos(x))^2+(sin((2pi)/9)-sin(x))^2 ?
The solution to expand (cos((2pi)/9)-cos(x))^2+(sin((2pi)/9)-sin(x))^2 is 2(1-cos((2pi)/9-x))