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Question

Find he value of: $$3\,\text{cosec}^{2}\,60^{\circ}\,-\,2\,\cot^{2}\,30^{\circ}\,+\,\sec^{2}\,45^{\circ}\,$$


Solution

$$3\,\text{cosec}^{2}\,60^{\circ}\,-\,2\,\cot^{2}\,30^{\circ}\,+\,\sec^{2}\,45^{\circ}\,=\,0$$
L.H.S. = $$3\,\text{cosec}^{2}\,60^{\circ}\,-\,2\,\cot^{2}\,30^{\circ}\,+\,\sec^{2}\,45^{\circ}$$
= $$3 (\dfrac{2}{\sqrt{3}})^2 - 2 (\sqrt{3})^2 + (\sqrt{2})^2$$
= $$ 3 (\dfrac{4}{3}) - 2 (3) + 2$$
= $$4 - 6  + 2$$
= $$0$$

Mathematics

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