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Equations involving sinx + cosx and sinx.cosx

If x'=n π/2 a...

Question

If $x \neq \frac{n π}{2}$ and $(cos x)^{{sin}^{2} x - 3 sin x + 2} = 1$ 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
As, $x \neq \frac{n π}{2},$ we get $cos x \neq 0, 1 - 1$
So, $s i n^{2} x - 3 sin x + 2 = 0$
$\Rightarrow sin x = 1, 2$
Which lis not possible as $x \neq \frac{n π}{2}$
$∴$ No solution.

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