1 / sqrt{1 + tan^2{theta}}

正文

这里简单推导一下这个式子。
1 1 + tan ⁡ 2 θ = 1 1 + sin ⁡ 2 θ cos ⁡ 2 θ = 1 cos ⁡ 2 θ + sin ⁡ 2 θ cos ⁡ 2 θ = 1 1 cos ⁡ 2 θ = 1 1 cos ⁡ θ = cos ⁡ θ \begin{align} \frac{1}{\sqrt{1+\tan^2{\theta}} } &= \frac{1}{\sqrt{1+\frac{\sin^2{\theta}}{\cos^2{\theta}} } } \nonumber \\ &= \frac{1}{\sqrt{\frac{\cos^2{\theta} + \sin^2{\theta}}{\cos^2{\theta}} } } \nonumber \\ &= \frac{1}{\sqrt{\frac{1}{\cos^2{\theta}} } } \nonumber \\ &= \frac{1}{\frac{1}{\cos{\theta}} } \nonumber \\ &= \c