First slide

Compound angles

Question

If $\cos 28^{\circ} + \sin 28^{\circ} = k^{3}, then \cos 17^{\circ}$ is equal to

Moderate

A

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

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

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

none of these

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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