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受欢迎的三角函数 >

1-sec^2(x)=tan^2(x)

解答

1 - sec^{2} (x) = tan^{2} (x)

解答

x = πn

+1

度数

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

求解步骤

1 - sec^{2} (x) = tan^{2} (x)

两边减去

tan^{2} (x)

1 - sec^{2} (x) - tan^{2} (x) = 0

使用三角恒等式改写

1 - sec^{2} (x) - tan^{2} (x)

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - 1 = tan^{2} (x)

= - tan^{2} (x) - tan^{2} (x)

化简

= - 2 tan^{2} (x)

- 2 tan^{2} (x) = 0

两边除以

- 2

- 2 tan^{2} (x) = 0

两边除以

- 2

- 2 tan^{2} (x) = 0

两边除以

- 2

\frac{- 2 tan ^{2} ( x )}{- 2} = \frac{0}{- 2}

化简

tan^{2} (x) = 0

tan^{2} (x) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

tan (x) = 0

tan (x) = 0

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 = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

作图

流行的例子

csc^2(x)=(1/(cos(x)))^2

csc^{2} (x) = (\frac{1}{cos ( x )})^{2}

-2cos^2(x)+3cos(x)=1

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

2-10sec(x)=4-9sec(x)

2 - 10 sec (x) = 4 - 9 sec (x)

7=e^{2sin(x)}+3

7 = e^{2 s i n (x)} + 3

sin (u) = - 0.9