Evaluate the following: 34^ 35^ 57^ 56^ - Vidyadip

Question

Evaluate the following$: \frac{\cos 34^{\circ} \cos 35^{\circ}}{\sin 57^{\circ} \sin 56^{\circ}}$

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Answer

$ \frac{\cos 34^{\circ} \cos 35^{\circ}}{\sin 57^{\circ} \sin 56^{\circ}}$
$ =\frac{\cos \left(90^{\circ}-56^{\circ}\right) \cos \left(90^{\circ}-57^{\circ}\right)}{\sin 57^{\circ} \sin 56^{\circ}}$
$ =\frac{\sin 56^{\circ} \sin 57^{\circ}}{\sin 57^{\circ} \sin 56^{\circ}}$
$ =1 .$

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