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受欢迎的三角函数 >

cos(x)((cos(x))/(sin(x)))+sin(x)=sec(x)

解答

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

解答

x = \frac{π}{4} + πn

+1

度数

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

求解步骤

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

两边减去

sec (x)

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

化简

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

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

将项转换为分式:

sin (x) = \frac{sin ( x ) sin ( x )}{sin ( x )}, sec (x) = \frac{sec ( x ) sin ( x )}{sin ( x )}

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

因为分母相等，所以合并分式:

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

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

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

cos^{2} (x) + sin (x) sin (x) - sec (x) sin (x)

sin (x) sin (x) = sin^{2} (x)

sin (x) sin (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

数字相加:

1 + 1 = 2

= sin^{2} (x)

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

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

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

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

cos^{2} (x) + sin^{2} (x) - sec (x) sin (x) = 0

使用三角恒等式改写

- sec (x) sin (x) + 1

sec (x) sin (x) = tan (x)

sec (x) sin (x)

用 sin, cos 表示

sec (x) sin (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

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

化简

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

\frac{1}{cos ( x )} sin (x)

分式相乘:

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

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

乘以:

1 \cdot sin (x) = sin (x)

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

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

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

使用基本三角恒等式:

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

= tan (x)

= 1 - tan (x)

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

两边除以

- 1

- tan (x) = - 1

两边除以

- 1

\frac{- tan ( x )}{- 1} = \frac{- 1}{- 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

sec(40+2θ)=csc(15)

sec (4 0^{\circ} + 2 θ) = csc (1 5^{\circ})

arcsin(x)-arccos(x)=arcsin(1/2)

arcsin (x) - arccos (x) = arcsin (\frac{1}{2})

3sin^2(x)+sin(x)-4=0

3 sin^{2} (x) + sin (x) - 4 = 0

2sin(x)+5cos(x)=4

2 sin (x) + 5 cos (x) = 4

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

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