# Simplify trig equation

#### korindou

$$\displaystyle \tan(2\Delta\theta) = \frac{D_1\sin(2\theta_2)-D_2\sin(2\theta_1)}{D_2\cos(2\theta_1)-D_1\cos(2\theta_2)}$$

I want to have an expression for delta theta. I know i can just take arctan for both sides, but i want right side part to be more simple because it would be computed often. Thanks.

#### idontknow

$$\displaystyle \sin(2\theta ) = 2\sin(\theta) \cos(\theta)$$ and $$\displaystyle \cos(2\theta ) =1-2\sin^2 ( \theta )$$.

#### korindou

$$\displaystyle \sin(2\theta ) = 2\sin(\theta) \cos(\theta)$$ and $$\displaystyle \cos(2\theta ) =1-2\sin^2 ( \theta )$$.
I guess expanding sin and cos will only make expression more complicated.

#### romsek

Math Team
how big do you expect these angles to be? If there are very small $\sin(x) \approx x,~\cos(x)\approx 1$

#### korindou

how big do you expect these angles to be? If there are very small $\sin(x) \approx x,~\cos(x)\approx 1$
From 0 to pi/2, so this really won't work