Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.
Option 1: $\frac{7}{6 \sqrt{3}}$
Option 2: $\frac{\sqrt{3}}{6}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{7}{2 \sqrt{3}}$
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Correct Answer: $\frac{7}{2 \sqrt{3}}$
Solution :
$\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$
= $1+\frac{\sqrt{3}}{2}-1+\frac{2}{\sqrt{3}}+0$
= $\frac{\sqrt{3}}{2}+\frac{2}{\sqrt{3}}$
= $\frac{3+4}{2\sqrt{3}}$
= $\frac{7}{2 \sqrt{3}}$
Hence, the correct answer is $\frac{7}{2 \sqrt{3}}$.
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