If sin (sinx + cosx) = cos(cosx – sinx), then the value of sinx can be -

$\frac{π}{4}$

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$\frac{\sqrt{16 - π^{2}}}{4}$

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$\frac{π}{8}$

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$- \frac{π}{4}$

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Solution

The correct options are
A
$\frac{π}{4}$

B
$\frac{\sqrt{16 - π^{2}}}{4}$

$c o s (c o s x - s i n x) = c o s (\frac{π}{2} - (s i n x + c o s x)) \Rightarrow c o s x - s i n x = 2 n π \pm (\frac{π}{2} - (s i n x + c o s x))$

$\begin{matrix} \Rightarrow c o s x = n π + \frac{π}{4} & s i n x = - n π + \frac{π}{4} C l e a r l y, n = 0 & c l e a r l y n = 0 \Rightarrow c o s x = \frac{π}{4} & \Rightarrow s i n x = \frac{π}{4} \end{matrix}$
$\Rightarrow s i n x = \pm \frac{\sqrt{16 - π^{2}}}{4}$

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