The value of $\left(\dfrac{1}{3}\cot^2 30^\circ - \dfrac{1}{2}\sec^...

Question

The value of $\left(\dfrac{1}{3}\cot^2 30^\circ - \dfrac{1}{2}\sec^2 60^\circ\right)$ is :

Accepted Answer

Step 1: $\cot 30^\circ = \sqrt{3}$ and $\sec 60^\circ = 2$.
Step 2: $$\frac{1}{3}\cot^2 30^\circ = \frac{1}{3}(\sqrt{3})^2 = \frac{3}{3} = 1$$
Step 3: $$\frac{1}{2}\sec^2 60^\circ = \frac{1}{2}(2)^2 = 2$$
Step 4: $$1 - 2 = -1$$

Correct option : (A)

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