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受欢迎的三角函数 >

2cos^2(x)+1=cos^2(x)

解答

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

解答

x \in R 无解

求解步骤

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

用替代法求解

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

令

: cos (x) = u

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

2 u^{2} + 1 = u^{2} : u = i, u = - i

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

将

1

到右边

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

两边减去

1

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

化简

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

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

将

u^{2}

para o lado esquerdo

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

两边减去

u^{2}

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

化简

u^{2} = - 1

u^{2} = - 1

对于

x^{2} = f (a)

解为

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

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

u = cos (x)

代回

cos (x) = i, cos (x) = - i

cos (x) = i, cos (x) = - i

cos (x) = i :

无解

cos (x) = i

无解

cos (x) = - i :

无解

cos (x) = - i

无解

合并所有解

x \in R 无解

作图

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