三角学 示例

使用基于 ${\displaystyle {\cot }^2\left(x\right)+1={\csc }^2\left(x\right)}$ 恒等式的 ${\displaystyle {\csc }^2\left(x\right)-1}$ 替换 ${\displaystyle {\cot }^2\left(x\right)}$。

重新排列多项式。

代入 ${\displaystyle u}$ 替换 ${\displaystyle \csc \left(x\right)}$。

在等式两边都加上 ${\displaystyle 5}$。

将 ${\displaystyle -1}$ 和 ${\displaystyle 5}$ 相加。

将 ${\displaystyle u+2}$ 设为等于 ${\displaystyle 0}$。

从等式两边同时减去 ${\displaystyle 2}$。

代入 ${\displaystyle \csc \left(x\right)}$ 替换 ${\displaystyle u}$。

取等式两边的反余割以从余割中提出 ${\displaystyle x}$。

The cosecant function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from ${\displaystyle 2\pi }$, to find a reference angle. Next, add this reference angle to ${\displaystyle \pi }$ to find the solution in the third quadrant.