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受欢迎的三角函数 >

cos^2(x)+1=4

解答

cos^{2} (x) + 1 = 4

解答

x \in R 无解

求解步骤

cos^{2} (x) + 1 = 4

用替代法求解

cos^{2} (x) + 1 = 4

令

: cos (x) = u

u^{2} + 1 = 4

u^{2} + 1 = 4 : u = 3, u = - 3

u^{2} + 1 = 4

将

1

到右边

u^{2} + 1 = 4

两边减去

1

u^{2} + 1 - 1 = 4 - 1

化简

u^{2} = 3

u^{2} = 3

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 3, u = - 3

u = cos (x)

代回

cos (x) = 3, cos (x) = - 3

cos (x) = 3, cos (x) = - 3

cos (x) = 3 :

无解

cos (x) = 3

- 1 \leq cos (x) \leq 1

无解

cos (x) = - 3 :

无解

cos (x) = - 3

- 1 \leq cos (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

1 = sin^{2} (x)

-2sin^2(x)-cos(x)=-1

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

tan^2(x)=1+sec(x)

tan^{2} (x) = 1 + sec (x)

8 sin^{2} (x) = 7

-6arcsin(3x)=pi

- 6 arcsin (3 x) = π