What is the value of \frac{\cos^{2}32^{\circ}+\cos^{2}58^{\circ}}{\sec^{2}50^{\circ}-\cot^{2}40^{\circ}} + 4\tan 13^{\circ}\tan 37^{\circ}\tan 53^{\circ}\tan 77^{\circ}?

Explanation

Since \cos 58^{\circ} = \sin 32^{\circ}, the numerator is \cos^2 32^{\circ} + \sin^2 32^{\circ} = 1. Since \cot 40^{\circ} = \tan 50^{\circ}, the denominator is \sec^2 50^{\circ} - \tan^2 50^{\circ} = 1. The first term is 1. For the second term, \tan 77^{\circ} = \cot 13^{\circ} and \tan 53^{\circ} = \cot 37^{\circ}, so their product is 4 \times 1 \times 1 = 4. Sum = 1 + 4 = 5.

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