If $\cos 28^{\circ} + \sin 28^{\circ} = k^{3}$ , then cos 17⁰ is equal to

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$- \frac{k^{3}}{\sqrt{2}}$

none of these

$\frac{k^{3}}{\sqrt{2}}$

$\pm \frac{k^{3}}{\sqrt{2}}$

answer is A.

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Detailed Solution

$\begin{matrix} \cos 17^{\circ} = \cos (45^{\circ} - 28^{\circ}) \\ = \cos 45^{\circ} \cos 28^{\circ} + \sin 45^{\circ} \sin 28^{\circ} \\ = \frac{\cos 28^{\circ} + \sin 28^{\circ}}{\sqrt{2}} = \frac{k^{3}}{\sqrt{2}} \end{matrix}$

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