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受欢迎的代数 >

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

解答

化简

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

解答

2 cos (x - y) + 2

求解步骤

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

展开

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

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

展开

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

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

= 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 sec(b)(cos(b)+sin(b))

e x p an d sec (b) (cos (b) + sin (b))

展开 (-3,5)y(-4,-1)

e x p an d (- 3, 5) y (- 4, - 1)

展开 ((2x+4))/(s(s^2+5))

e x p an d \frac{( 2 x + 4 )}{s ( s ^{2} + 5 )}

展开 sin(y)(e^x+e^xy)

e x p an d sin (y) (e^{x} + e^{x} y)

展开 xy+(2x^2+3y^2-20)(dy)/(dx)

e x p an d x y + (2 x^{2} + 3 y^{2} - 20) \frac{d y}{d x}