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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

The sum of al...

Question

The sum of all the solutions of the equation $cos 2 x + {sin}^{2} 2 x = 1$ which lie in the interval $[0, 2 π]$ is equal to

4 π

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5 π

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7 π

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8 π

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Solution

The correct option is C $7 π$
$cos 2 x (1 - cos 2 x) = 0$
$\Rightarrow cos 2 x = 0, 1$
$cos 2 x = 0 \Rightarrow 2 x = \frac{π}{2}, \frac{3 π}{2}, \frac{5 π}{2}, \frac{7 π}{2}$
$cos 2 x = 1 \Rightarrow 2 x = 0, 2 π, 4 π$
Required sum $= 7 π$

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