If `acos2theta+bsin2theta= c, alpha and beta` as its roots , then prove that `tanalpha+t a nbeta=(2 b)/(a+c)`, `tanalpha*t a nbeta=(c-a)/(c+a)` , `tan(alpha+beta)=b/a`

Explanation

To prove the given equations based on the equation \( a \cos 2\theta + b \sin 2\theta = c \) where \( \alpha \) and \( \beta \) are its roots, we will follow these steps:

### Step 1: Rewrite the equation in terms of tangent
We start with the equation:
\[ a \cos 2\theta + b \sin 2\theta = c \]
Using the identities \( \cos 2\theta = \frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} \) and \( \sin 2\theta = \frac{2 \tan \theta}{1 + \tan^2 \theta} \), we can rewrite the equation as:
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