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受欢迎的三角函数 >

8sin^2(x)+6cos^2(x)=10

解答

8 sin^{2} (x) + 6 cos^{2} (x) = 10

解答

x \in R 无解

求解步骤

8 sin^{2} (x) + 6 cos^{2} (x) = 10

两边减去

10

8 sin^{2} (x) + 6 cos^{2} (x) - 10 = 0

使用三角恒等式改写

- 10 + 6 cos^{2} (x) + 8 sin^{2} (x)

使用毕达哥拉斯恒等式:

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

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

= - 10 + 6 (1 - sin^{2} (x)) + 8 sin^{2} (x)

化简

- 10 + 6 (1 - sin^{2} (x)) + 8 sin^{2} (x) : 2 sin^{2} (x) - 4

- 10 + 6 (1 - sin^{2} (x)) + 8 sin^{2} (x)

乘开

6 (1 - sin^{2} (x)) : 6 - 6 sin^{2} (x)

6 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 6, b = 1, c = sin^{2} (x)

= 6 \cdot 1 - 6 sin^{2} (x)

数字相乘:

6 \cdot 1 = 6

= 6 - 6 sin^{2} (x)

= - 10 + 6 - 6 sin^{2} (x) + 8 sin^{2} (x)

化简

- 10 + 6 - 6 sin^{2} (x) + 8 sin^{2} (x) : 2 sin^{2} (x) - 4

- 10 + 6 - 6 sin^{2} (x) + 8 sin^{2} (x)

同类项相加:

- 6 sin^{2} (x) + 8 sin^{2} (x) = 2 sin^{2} (x)

= - 10 + 6 + 2 sin^{2} (x)

数字相加/相减:

- 10 + 6 = - 4

= 2 sin^{2} (x) - 4

= 2 sin^{2} (x) - 4

= 2 sin^{2} (x) - 4

- 4 + 2 sin^{2} (x) = 0

用替代法求解

- 4 + 2 sin^{2} (x) = 0

令

: sin (x) = u

- 4 + 2 u^{2} = 0

- 4 + 2 u^{2} = 0 : u = 2, u = - 2

- 4 + 2 u^{2} = 0

将

4

到右边

- 4 + 2 u^{2} = 0

两边加上

4

- 4 + 2 u^{2} + 4 = 0 + 4

化简

2 u^{2} = 4

2 u^{2} = 4

两边除以

2

2 u^{2} = 4

两边除以

2

\frac{2 u ^{2}}{2} = \frac{4}{2}

化简

u^{2} = 2

u^{2} = 2

对于

x^{2} = f (a)

解为

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

u = 2, u = - 2

u = sin (x)

代回

sin (x) = 2, sin (x) = - 2

sin (x) = 2, sin (x) = - 2

sin (x) = 2 :

无解

sin (x) = 2

- 1 \leq sin (x) \leq 1

无解

sin (x) = - 2 :

无解

sin (x) = - 2

- 1 \leq sin (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

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