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Question

Find the value of $$(\sin^{2}\, 30^{\circ} +\cos^{2} 30^{\circ} +\cot^{2}\, 45^{\circ})$$


Solution

$$\sin^2 30^{\circ} + \cos^2 30^{\circ} + \cot^2 45^{\circ}$$
= $$(\cfrac{1}{2})^2 + (\cfrac{\sqrt{3}}{2})^2 + 1^2$$
= $$\cfrac{1}{4} + \cfrac{3}{4} + 1$$
= $$\cfrac{1 + 3 + 4}{4}$$
= $$\cfrac{8}{4}$$
= $$2$$

Mathematics

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