Which of the following is not the value of sin 27⁰ - cos 27⁰?

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$- \frac{\sqrt{3 - \sqrt{5}}}{2}$

$- \frac{\sqrt{5 - \sqrt{5}}}{2}$

$- \frac{\sqrt{5} - 1}{2 \sqrt{2}}$

none of these

answer is B.

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Detailed Solution

$\begin{matrix} \sin 27^{\circ} - \sin 63^{\circ} = - 2 \cos 45^{\circ} \sin 18^{\circ} \\ = - \sqrt{2} (\frac{\sqrt{5} - 1}{4}) = - \frac{\sqrt{5} - 1}{2 \sqrt{2}} = - \frac{\sqrt{3 - \sqrt{5}}}{2} \end{matrix}$

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