The number of solutions of $s i n^{3} x c o s x + s i n^{2} x c o s^{2} x + s i n x c o s^{3} x = 1$ in $[0, 2 π]$ is-

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Solution

The correct option is D 0
$s i n x c o s x [s i n^{2} x + s i n x c o s x + c o s^{2} x] = 1 \Rightarrow s i n x c o s x + (s i n x c o s x)^{2} = 1$
$s i n^{2} 2 x + 2 s i n 2 x - 4 = 0 \Rightarrow s i n 2 x = \frac{- 2 \pm \sqrt{4 + 16}}{2} = - 1 \pm \sqrt{5}$ , which is not possible.
Hence (D) is the correct answer.

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