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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

If x'=n π/2 a...

Question

If $x \neq \frac{n π}{2} a n d (c o s x)^{s i n^{2} x - 3 s i n x + 2} = 1$ then all solutions of x are given by

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None of these

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Solution

The correct option is D
None of these

If $x \neq \frac{n π}{2} c o s x \neq 0, 1, - 1$
So $s i n^{2} x - 3 s i n x + 2 = 0$
$\Rightarrow s i n x = 1, 2$ which is not possible as $x \neq \frac{n π}{2}$

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