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

The solution to (sin(x)-sin(y))^2+(cos(x)-cos(y))^2 is -2cos(x-y)+2

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simplify (sin(x)-sin(y))^2+(cos(x)-cos(y))^2

simplify

(sin (x) - sin (y))^{2} + (cos (x) - cos (y))^{2}

- 2 cos (x - y) + 2

Solution steps

(sin (x) - sin (y))^{2} + (cos (x) - cos (y))^{2}

Expand

(sin (x) - sin (y))^{2} : sin^{2} (x) - 2 sin (x) sin (y) + sin^{2} (y)

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

Expand

(cos (x) - cos (y))^{2} : cos^{2} (x) - 2 cos (x) cos (y) + cos^{2} (y)

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

Use the Pythagorean identity:

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

= - 2 cos (x) cos (y) - 2 sin (x) sin (y) + 1 + 1

Add the numbers:

1 + 1 = 2

= - 2 cos (x) cos (y) - 2 sin (x) sin (y) + 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 (x - y))

Factor

- 2 cos (x) cos (y) - 2 sin (x) sin (y) + 2 : 2 (- cos (x) cos (y) - sin (x) sin (y) + 1)

= 2 (- cos (x - y) + 1)

Expand

2 (- cos (x - y) + 1) : - 2 cos (x - y) + 2

= - 2 cos (x - y) + 2

\frac{2 ( 9 x ^{2} - 24 x - 16 )}{3 x - 4}

\frac{\partial}{\partial x} ((z) (x^{2} + 3 x y + y^{2}))

k q (\frac{1}{x} - \frac{1}{b d})

\frac{n ( n + 1 ) ( 2 n + 1 )}{6} + 3 (\frac{n ( n + 1 )}{2})

(1, - i) (2, - 1)

What is (sin(x)-sin(y))^2+(cos(x)-cos(y))^2 ?
The solution to (sin(x)-sin(y))^2+(cos(x)-cos(y))^2 is -2cos(x-y)+2