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If acos2theta+bsin2theta=c has alpha an...

If `acos2theta+bsin2theta=c ` has `alpha and beta` as its roots, then prove that `tanalpha+tanbeta=(2b)/(a+c)`.

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To prove that if \( a \cos 2\theta + b \sin 2\theta = c \) has roots \( \alpha \) and \( \beta \), then \( \tan \alpha + \tan \beta = \frac{2b}{a+c} \), we can follow these steps: ### Step 1: Rewrite the Given Equation We start with the equation: \[ a \cos 2\theta + b \sin 2\theta = c \] Using the double angle identities, we can express \( \cos 2\theta \) and \( \sin 2\theta \) in terms of \( \tan \theta \): ...
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