化简 (t-sin(t))^2+(1-cos(t))^2

解答

化简

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

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

求解步骤

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

展开

(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}

展开

(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)

使用毕达哥拉斯恒等式:

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

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

数字相加:

1 + 1 = 2

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

s im pl i f y (x + 3 y^{4}) (x - 3 y^{4})

e x p an d - \frac{r}{8} (2 s - 8)

e x p an d 2 (x + δ x)^{5}

e x p an d (1 - \frac{x ^{2}}{2})^{2}

s im pl i f y (2 p + \frac{3}{4}) (2 p - \frac{3}{4})