AP ICET 2014 Question Paper

Question 118

$$\sin 120^\circ \cos 60^\circ \cot 30^\circ \cosec^2 30^\circ =$$

Solution

$$\sin120^{\circ\ }\cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }=\sin\left(90+30^{\circ\ }\right)\cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }$$

$$=\cos30^{\circ\ }\ \cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }$$

$$=\frac{\sqrt{\ 3}}{2}\times\ \frac{1}{2}\times\ \sqrt{\ 3}\times\ 4$$

$$=3$$

Hence, the correct answer is Option B

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