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受欢迎的三角函数 >

sqrt(3)sin(2x)+cos(2x)=2cos(2x)

解答

3 sin (2 x) + cos (2 x) = 2 cos (2 x)

解答

x = \frac{π}{12} + \frac{πn}{2}

+1

度数

x = 1 5^{\circ} + 9 0^{\circ} n

求解步骤

3 sin (2 x) + cos (2 x) = 2 cos (2 x)

两边减去

2 cos (2 x)

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

使用三角恒等式改写

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

在两边除以

cos (2 x), cos (2 x) \neq = 0

\frac{3 sin ( 2 x ) - cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

化简

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

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 tan (2 x) - 1 = 0

3 tan (2 x) - 1 = 0

将

1

到右边

3 tan (2 x) - 1 = 0

两边加上

1

3 tan (2 x) - 1 + 1 = 0 + 1

化简

3 tan (2 x) = 1

3 tan (2 x) = 1

两边除以

3

3 tan (2 x) = 1

两边除以

3

\frac{3 tan ( 2 x )}{3} = \frac{1}{3}

化简

\frac{3 tan ( 2 x )}{3} = \frac{1}{3}

化简

\frac{3 tan ( 2 x )}{3} : tan (2 x)

\frac{3 tan ( 2 x )}{3}

约分:

3

= tan (2 x)

化简

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

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

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

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

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

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}

2 x = \frac{π}{6} + πn

2 x = \frac{π}{6} + πn

解

2 x = \frac{π}{6} + πn : x = \frac{π}{12} + \frac{πn}{2}

2 x = \frac{π}{6} + πn

两边除以

2

2 x = \frac{π}{6} + πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{π}{6}}{2} + \frac{πn}{2} : \frac{π}{12} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

作图

流行的例子

sin(x+pi/2)=(sqrt(3))/2

sin (x + \frac{π}{2}) = \frac{3}{2}

sqrt(3)tan(2x)=-1

3 tan (2 x) = - 1

2 tan^{2} (3 x) = 6

5cos(x)+1=-2sin^2(x)

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

tan (x) = \frac{19}{11}