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受欢迎的三角函数 >

sin^2(a)=2sin^2(a)+3

解答

sin^{2} (a) = 2 sin^{2} (a) + 3

解答

a \in R 无解

求解步骤

sin^{2} (a) = 2 sin^{2} (a) + 3

用替代法求解

sin^{2} (a) = 2 sin^{2} (a) + 3

令

: sin (a) = u

u^{2} = 2 u^{2} + 3

u^{2} = 2 u^{2} + 3 : u = 3 i, u = - 3 i

u^{2} = 2 u^{2} + 3

将

2 u^{2}

para o lado esquerdo

u^{2} = 2 u^{2} + 3

两边减去

2 u^{2}

u^{2} - 2 u^{2} = 2 u^{2} + 3 - 2 u^{2}

化简

- u^{2} = 3

- u^{2} = 3

两边除以

- 1

- u^{2} = 3

两边除以

- 1

\frac{- u ^{2}}{- 1} = \frac{3}{- 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

化简

- 3 : 3 i

- 3

使用根式运算法则:

- a = - 1 a

- 3 = - 1 3

= - 1 3

使用虚数运算法则:

- 1 = i

= 3 i

化简

- - 3 : - 3 i

- - 3

化简

- 3 : 3 i

- 3

使用根式运算法则:

- a = - 1 a

- 3 = - 1 3

= - 1 3

使用虚数运算法则:

- 1 = i

= 3 i

= - 3 i

u = 3 i, u = - 3 i

u = sin (a)

代回

sin (a) = 3 i, sin (a) = - 3 i

sin (a) = 3 i, sin (a) = - 3 i

sin (a) = 3 i :

无解

sin (a) = 3 i

无解

sin (a) = - 3 i :

无解

sin (a) = - 3 i

无解

合并所有解

a \in R 无解

作图

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