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受欢迎的三角函数 >

2(tan(x)+1)+3(1-tan(x))<-2(tan(x)-3)

解答

2 (tan (x) + 1) + 3 (1 - tan (x)) < - 2 (tan (x) - 3)

解答

- \frac{π}{2} + πn < x < \frac{π}{4} + πn

+2

间隔符号

(- \frac{π}{2} + πn, \frac{π}{4} + πn)

十进制

- 1.57079 \dots + πn < x < 0.78539 \dots + πn

求解步骤

2 (tan (x) + 1) + 3 (1 - tan (x)) < - 2 (tan (x) - 3)

令

: u = tan (x)

2 (u + 1) + 3 (1 - u) < - 2 (u - 3)

2 (u + 1) + 3 (1 - u) < - 2 (u - 3) : u < 1

2 (u + 1) + 3 (1 - u) < - 2 (u - 3)

展开

2 (u + 1) + 3 (1 - u) : - u + 5

2 (u + 1) + 3 (1 - u)

乘开

2 (u + 1) : 2 u + 2

2 (u + 1)

使用分配律:

a (b + c) = ab + a c

a = 2, b = u, c = 1

= 2 u + 2 \cdot 1

数字相乘:

2 \cdot 1 = 2

= 2 u + 2

= 2 u + 2 + 3 (1 - u)

乘开

3 (1 - u) : 3 - 3 u

3 (1 - u)

使用分配律:

a (b - c) = ab - a c

a = 3, b = 1, c = u

= 3 \cdot 1 - 3 u

数字相乘:

3 \cdot 1 = 3

= 3 - 3 u

= 2 u + 2 + 3 - 3 u

化简

2 u + 2 + 3 - 3 u : - u + 5

2 u + 2 + 3 - 3 u

对同类项分组

= 2 u - 3 u + 2 + 3

同类项相加:

2 u - 3 u = - u

= - u + 2 + 3

数字相加:

2 + 3 = 5

= - u + 5

= - u + 5

展开

- 2 (u - 3) : - 2 u + 6

- 2 (u - 3)

使用分配律:

a (b - c) = ab - a c

a = - 2, b = u, c = 3

= - 2 u - (- 2) \cdot 3

使用加减运算法则

- (- a) = a

= - 2 u + 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= - 2 u + 6

- u + 5 < - 2 u + 6

将

5

到右边

- u + 5 < - 2 u + 6

两边减去

5

- u + 5 - 5 < - 2 u + 6 - 5

化简

- u < - 2 u + 1

- u < - 2 u + 1

将

2 u

para o lado esquerdo

- u < - 2 u + 1

两边加上

2 u

- u + 2 u < - 2 u + 1 + 2 u

化简

u < 1

u < 1

u < 1

u = tan (x)

代回

tan (x) < 1

若

tan (x) < a

，则

- \frac{π}{2} + πn < x < arctan (a) + πn

- \frac{π}{2} + πn < x < arctan (1) + πn

化简

arctan (1) : \frac{π}{4}

arctan (1)

使用以下普通恒等式:

arctan (1) = \frac{π}{4}

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

- \frac{π}{2} + πn < x < \frac{π}{4} + πn

流行的例子

cot (x) > 1

cos(2x)<=-sin(x)-2

cos (2 x) \leq - sin (x) - 2

sin(x)*cos(2x)>0

sin (x) \cdot cos (2 x) > 0

cos^{2} (x) > \frac{3}{4}

(3sin(x)-sqrt(3)cos(x))/(2cos(x)+1)<0

\frac{3 sin ( x ) - 3 cos ( x )}{2 cos ( x ) + 1} < 0