If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation a $\displaystyle \cos : 2 \theta + b : \sin : 2\theta = c$ then $\displaystyle \cos^2\alpha + \cos^2\beta$ is equal to
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$\displaystyle \frac {a^2 + ac + b^2}{a^2 + b^2}$
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$\displaystyle \frac {a^2 - ac + b^2}{a^2 + b^2}$
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$\displaystyle \frac {2b^2}{a^2 + c^2}$
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$\displaystyle \frac {2a^2}{b^2 + c^2}$
A
Correct answer
Explanation
Given a cos(2theta) + b sin(2theta) = c, use the identities cos(2theta) = 2cos^2(theta) - 1 and sin(2theta) = 2sin(theta)cos(theta). This leads to a quadratic in tan(theta) or similar. The sum of cos^2(alpha) + cos^2(beta) for such equations is a standard result derived from the roots of the quadratic equation.