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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{3 π}{4} + πn

+1

度数

x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

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

两边减去

tan (x) cos (x) - cos (x)

2 sin (x) - tan (x) cos (x) + cos (x) = 0

使用三角恒等式改写

cos (x) + 2 sin (x) - cos (x) tan (x)

使用基本三角恒等式:

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

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

化简

cos (x) + 2 sin (x) - cos (x) \frac{sin ( x )}{cos ( x )} : cos (x) + sin (x)

cos (x) + 2 sin (x) - cos (x) \frac{sin ( x )}{cos ( x )}

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

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

分式相乘:

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

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

约分:

cos (x)

= sin (x)

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

同类项相加:

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

= cos (x) + sin (x)

= cos (x) + sin (x)

在两边除以

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

\frac{cos ( x ) + sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

1 + \frac{sin ( x )}{cos ( x )} = 0

使用基本三角恒等式:

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

1 + tan (x) = 0

1 + tan (x) = 0

将

1

到右边

1 + tan (x) = 0

两边减去

1

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

化简

tan (x) = - 1

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

作图

流行的例子

cos(θ)-sin(θ)=1,0<= θ<= 2pi

cot(θ-pi/2)=1.07

2^{arccos(x)}+4^{arccos(x)+1}-2=3