What is (t-sin(t))^2+(1-cos(t))^2 ?

The solution to (t-sin(t))^2+(1-cos(t))^2 is t^2-2tsin(t)-2cos(t)+2

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simplify (t-sin(t))^2+(1-cos(t))^2

simplify

(t - sin (t))^{2} + (1 - cos (t))^{2}

t^{2} - 2 t sin (t) - 2 cos (t) + 2

Solution steps

(t - sin (t))^{2} + (1 - cos (t))^{2}

Expand

(t - sin (t))^{2} : t^{2} - 2 t sin (t) + sin^{2} (t)

= t^{2} - 2 t sin (t) + sin^{2} (t) + (1 - cos (t))^{2}

Expand

(1 - cos (t))^{2} : 1 - 2 cos (t) + cos^{2} (t)

= t^{2} - 2 t sin (t) + sin^{2} (t) + 1 - 2 cos (t) + cos^{2} (t)

Use the Pythagorean identity:

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

= t^{2} - 2 t sin (t) - 2 cos (t) + 1 + 1

Add the numbers:

1 + 1 = 2

= t^{2} - 2 t sin (t) - 2 cos (t) + 2

(x + 3 y^{4}) (x - 3 y^{4})

- \frac{r}{8} (2 s - 8)

2 (x + δ x)^{5}

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

(2 p + \frac{3}{4}) (2 p - \frac{3}{4})

What is (t-sin(t))^2+(1-cos(t))^2 ?
The solution to (t-sin(t))^2+(1-cos(t))^2 is t^2-2tsin(t)-2cos(t)+2