Problem
15. Which of the following is equal to $\left(\operatorname{cosec} 30^{\circ}\right)\left(\cos 60^{\circ}\right)\left(\tan 45^{\circ}\right)\left(\sin 90^{\circ}\right)\left(\sec 45^{\circ}\right)$ ? 1. $1 / 2$ II. 1 III. 0 IV. $\sqrt{2}$ A. I only B. II only C. III only D. IV only
Solution
Step 1 ：Calculate the values of the trigonometric functions: \(\operatorname{cosec} 30^\circ = 2\), \(\cos 60^\circ = \frac{1}{2}\), \(\tan 45^\circ = 1\), \(\sin 90^\circ = 1\), \(\sec 45^\circ = \sqrt{2}\)
Step 2 ：Multiply the values together: \(2 \times \frac{1}{2} \times 1 \times 1 \times \sqrt{2} = \boxed{\sqrt{2}}\)
