If a cos 2 theta + b sin 2 theta = c has alph | vedclass

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(A) Given the equation: $a \cos 2 	heta + b \sin 2 	heta = c$ Using the identities $\cos 2 	heta = \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta}$ and

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$\frac{2 b}{c+a}$

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(A) Given the equation: $a \cos 2 	heta + b \sin 2 	heta = c$ Using the identities $\cos 2 	heta = \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta}$ and $\sin 2 	heta = \frac{2 	an 	heta}{1 + 	an^2 	heta}$,we get: $a \left( \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta} ight) + b \left( \frac{2 	an 	heta}{1 + 	an^2 	heta} ight) = c$ Multiplying both sides by $(1 + 	an^2 	heta)$: $a(1 - 	an^2 	heta) + 2b 	an 	heta = c(1 + 	an^2 	heta)$ $a - a 	an^2 	heta + 2b 	an 	heta = c + c 	an^2 	heta$ Rearranging the terms to form a quadratic equation in $	an 	heta$: $(a + c) 	an^2 	heta - 2b 	an 	heta + (c - a) = 0$ Since $\alpha$ and $\beta$ are the roots,$	an \alpha$ and $	an \beta$ are the roots of this quadratic equation. Using the sum of roots formula for $Ax^2 + Bx + C = 0$,which is $-\frac{B}{A}$: $	an \alpha + 	an \beta = -\frac{-2b}{a + c} = \frac{2b}{c + a}$

If $a \cos 2 \theta + b \sin 2 \theta = c$ has $\alpha$ and $\beta$ as its roots,then the value of $\tan \alpha + \tan \beta$ is

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