zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

4tan(x)=2sec^2(x)

解答

4 tan (x) = 2 sec^{2} (x)

解答

x = \frac{π}{4} + πn

+1

度数

x = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

4 tan (x) = 2 sec^{2} (x)

两边减去

2 sec^{2} (x)

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

使用三角恒等式改写

- 2 sec^{2} (x) + 4 tan (x)

使用毕达哥拉斯恒等式:

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

= - 2 (tan^{2} (x) + 1) + 4 tan (x)

- (1 + tan^{2} (x)) \cdot 2 + 4 tan (x) = 0

用替代法求解

- (1 + tan^{2} (x)) \cdot 2 + 4 tan (x) = 0

令

: tan (x) = u

- (1 + u^{2}) \cdot 2 + 4 u = 0

- (1 + u^{2}) \cdot 2 + 4 u = 0 : u = 1

- (1 + u^{2}) \cdot 2 + 4 u = 0

展开

- (1 + u^{2}) \cdot 2 + 4 u : - 2 - 2 u^{2} + 4 u

- (1 + u^{2}) \cdot 2 + 4 u

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

乘开

- 2 (1 + u^{2}) : - 2 - 2 u^{2}

- 2 (1 + u^{2})

使用分配律:

a (b + c) = ab + a c

a = - 2, b = 1, c = u^{2}

= - 2 \cdot 1 + (- 2) u^{2}

使用加减运算法则

+ (- a) = - a

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

数字相乘:

2 \cdot 1 = 2

= - 2 - 2 u^{2}

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

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

改写成标准形式

a x^{2} + b x + c = 0

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

使用求根公式求解

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

二次方程求根公式:

若

a = - 2, b = 4, c = - 2

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 2 ) ( - 2 )}{2 ( - 2 )}

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 2 ) ( - 2 )}{2 ( - 2 )}

4^{2} - 4 (- 2) (- 2) = 0

4^{2} - 4 (- 2) (- 2)

使用法则

- (- a) = a

= 4^{2} - 4 \cdot 2 \cdot 2

数字相乘:

4 \cdot 2 \cdot 2 = 16

= 4^{2} - 16

4^{2} = 16

= 16 - 16

数字相减:

16 - 16 = 0

= 0

u_{1, 2} = \frac{- 4 \pm 0}{2 ( - 2 )}

u = \frac{- 4}{2 ( - 2 )}

\frac{- 4}{2 ( - 2 )} = 1

\frac{- 4}{2 ( - 2 )}

去除括号:

(- a) = - a

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 4}{- 4}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4}{4}

使用法则

\frac{a}{a} = 1

= 1

u = 1

二次方程组的解是:

u = 1

u = tan (x)

代回

tan (x) = 1

tan (x) = 1

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 1

tan (x) = 1

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

合并所有解

x = \frac{π}{4} + πn

作图

流行的例子

sin(x)+cos(x)+cot(x)=csc(x)

sin (x) + cos (x) + cot (x) = csc (x)

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

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

cos(x)= 3/(sqrt(13))

cos (x) = \frac{3}{13}

3tan^3(x)-9tan(x)=0

3 tan^{3} (x) - 9 tan (x) = 0

cot(θ)=-1,cos(θ),90<θ<180

cot (θ) = - 1, cos (θ), 9 0^{\circ} < θ < 18 0^{\circ}