Question
Evaluate the following$: \sin35^\circ \sin45^\circ \sec55^\circ \sec45^\circ $
✓
Answer
$ \sin 35^{\circ} \sin 45^{\circ} \sec 55^{\circ} \sec 45^{\circ}$
$ =\sin \left(90^{\circ}-55^{\circ}\right) \times \frac{1}{\sqrt{2}} \times \frac{1}{\cos 55^{\circ}} \times \sqrt{2}$
$ =\cos 55^{\circ} \times \frac{1}{\cos 55^{\circ}} \times \frac{1}{\sqrt{2}} \times \sqrt{2}$
$ =1 .$
$ =\sin \left(90^{\circ}-55^{\circ}\right) \times \frac{1}{\sqrt{2}} \times \frac{1}{\cos 55^{\circ}} \times \sqrt{2}$
$ =\cos 55^{\circ} \times \frac{1}{\cos 55^{\circ}} \times \frac{1}{\sqrt{2}} \times \sqrt{2}$
$ =1 .$
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