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受欢迎的代数 >

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

解答

化简

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

解答

- 2 cos (x - y) + 2

求解步骤

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

展开

(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}

展开

(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)

使用毕达哥拉斯恒等式:

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

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

数字相加:

1 + 1 = 2

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

使用角差恒等式:

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))

分解

- 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)

展开

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

= - 2 cos (x - y) + 2

流行的例子

展开 (2(9x^2-24x-16))/(3x-4)

e x p an d \frac{2 ( 9 x ^{2} - 24 x - 16 )}{3 x - 4}

展开 (n(n+1)(2n+1))/6+3((n(n+1))/2)

e x p an d \frac{n ( n + 1 ) ( 2 n + 1 )}{6} + 3 (\frac{n ( n + 1 )}{2})

展开 (1,-i)(2,-1)

e x p an d (1, - i) (2, - 1)

展开 (e^{2s})/(s^2(s-1))

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

展开 (12-x)ln(x+8)

e x p an d (12 - x) ln (x + 8)