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受欢迎的三角函数 >

-(cos(x)-sin(x))/(1+sin(2x))=0

解答

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

解答

x = \frac{π}{4} + πn

+1

度数

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

求解步骤

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

使用三角恒等式改写

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

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

两边加上

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{π}{4} + πn

x = \frac{π}{4} + πn

作图

流行的例子

sqrt(2)cos(x)=cot(x)

2 cos (x) = cot (x)

tan(x)=(60}{\frac{(-20-90))/2}

tan (x) = \frac{60}{\frac{( - 20 - 90 )}{2}}

0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0

0.1 \cdot sin (θ) cos (53.1 3^{\circ}) + 0.1 \cdot sin (θ) = 0

tan (θ) = (1)

sec^2(x)=(3sqrt(3))/pi

sec^{2} (x) = \frac{3 3}{π}