Problem

\( \frac{\sin 770^{\circ}}{\cos 65^{\circ}-\sin 205^{\circ}} \)

Answer

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Answer

\( -\frac{\sqrt{6} - \sqrt{2}}{4} \)

Steps

Step 1 ：\( \frac{\sin (360^{\circ} \times 2 + 50^{\circ})}{\cos 65^{\circ} - \sin (180^{\circ} + 25^{\circ})} \)

Step 2 ：\( \frac{\sin 50^{\circ}}{\cos 65^{\circ} - (- \cos 25^{\circ})} \)

Step 3 ：\( -\frac{\sqrt{6} - \sqrt{2}}{4} \)

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