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受欢迎的代数 >

化简 (cos(x)-tan(x))^2+(sin(x)+1)^2

解答

化简

(cos (x) - tan (x))^{2} + (sin (x) + 1)^{2}

解答

tan^{2} (x) + 2

求解步骤

(cos (x) - tan (x))^{2} + (sin (x) + 1)^{2}

展开

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

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

展开

(sin (x) + 1)^{2} : sin^{2} (x) + 2 sin (x) + 1

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

使用毕达哥拉斯恒等式:

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

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

数字相加:

1 + 1 = 2

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

cos (x) tan (x) = sin (x)

= tan^{2} (x) + 2 sin (x) - 2 sin (x) + 2

同类项相加:

2 sin (x) - 2 sin (x) = 0

= tan^{2} (x) + 2

流行的例子

展开 (3a-5b)^3

e x p an d (3 a - 5 b)^{3}

化简 (sqrt(a)+2sqrt(y))/(sqrt(a)-2\sqrt{y)}

s im pl i f y \frac{a + 2 y}{a - 2 y}

化简 1-1/(1-1/2)

s im pl i f y 1 - \frac{1}{1 - \frac{1}{2}}

化简 (1-cos(2x))^3

s im pl i f y (1 - cos (2 x))^{3}

化简 (5x-6y)2

s im pl i f y (5 x - 6 y) 2