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受欢迎的三角函数 >

csc^2(x)+3cot^2(x)=1

解答

csc^{2} (x) + 3 cot^{2} (x) = 1

解答

x = \frac{π}{2} + πn

+1

度数

x = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

csc^{2} (x) + 3 cot^{2} (x) = 1

两边减去

1

csc^{2} (x) + 3 cot^{2} (x) - 1 = 0

使用三角恒等式改写

- 1 + csc^{2} (x) + 3 cot^{2} (x)

使用毕达哥拉斯恒等式:

csc^{2} (x) = 1 + cot^{2} (x)

csc^{2} (x) - 1 = cot^{2} (x)

= 3 cot^{2} (x) + cot^{2} (x)

化简

= 4 cot^{2} (x)

4 cot^{2} (x) = 0

两边除以

4

4 cot^{2} (x) = 0

两边除以

4

4 cot^{2} (x) = 0

两边除以

4

\frac{4 cot ^{2} ( x )}{4} = \frac{0}{4}

化简

cot^{2} (x) = 0

cot^{2} (x) = 0

使用法则

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

cot (x) = 0

cot (x) = 0

的通解

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

作图

流行的例子

2sin^2(θ)-sin(θ)-3=0

2 sin^{2} (θ) - sin (θ) - 3 = 0

4sin(x)cos(x)+1=0

4 sin (x) cos (x) + 1 = 0

4sin(x)=3csc(x)

4 sin (x) = 3 csc (x)

sin(2θ)=(sqrt(3))/2 ,0<= θ<2pi

sin (2 θ) = \frac{3}{2}, 0 \leq θ < 2 π

- sin (4 x) = 0