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受欢迎的三角函数 >

4sec^2(x)-3=0

解答

4 sec^{2} (x) - 3 = 0

解答

x \in R 无解

求解步骤

4 sec^{2} (x) - 3 = 0

用替代法求解

4 sec^{2} (x) - 3 = 0

令

: sec (x) = u

4 u^{2} - 3 = 0

4 u^{2} - 3 = 0 : u = \frac{3}{2}, u = - \frac{3}{2}

4 u^{2} - 3 = 0

将

3

到右边

4 u^{2} - 3 = 0

两边加上

3

4 u^{2} - 3 + 3 = 0 + 3

化简

4 u^{2} = 3

4 u^{2} = 3

两边除以

4

4 u^{2} = 3

两边除以

4

\frac{4 u ^{2}}{4} = \frac{3}{4}

化简

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

对于

x^{2} = f (a)

解为

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

u = \frac{3}{4}, u = - \frac{3}{4}

\frac{3}{4} = \frac{3}{2}

\frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

- \frac{3}{4} = - \frac{3}{2}

- \frac{3}{4}

化简

\frac{3}{4} : \frac{3}{2}

\frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= - \frac{3}{2}

u = \frac{3}{2}, u = - \frac{3}{2}

u = sec (x)

代回

sec (x) = \frac{3}{2}, sec (x) = - \frac{3}{2}

sec (x) = \frac{3}{2}, sec (x) = - \frac{3}{2}

sec (x) = \frac{3}{2} :

无解

sec (x) = \frac{3}{2}

sec (x) \leq - 1 or sec (x) \geq 1

无解

sec (x) = - \frac{3}{2} :

无解

sec (x) = - \frac{3}{2}

sec (x) \leq - 1 or sec (x) \geq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

cos^2(x)= 1/4 ,0<= x<= 2pi

cos^{2} (x) = \frac{1}{4}, 0 \leq x \leq 2 π

sin (θ) = - \frac{4}{9}

0 = 2 + 4 sin (θ)

cos (x) = \frac{71}{81}

2sin^2(2x)-sin(2x)-3=0

2 sin^{2} (2 x) - sin (2 x) - 3 = 0