Question 130

If tan $$\begin{bmatrix}\frac{\pi}{2}-\frac{\alpha}{2}\end{bmatrix}=\sqrt{3}$$, then the value of cos $$\alpha$$ is

Solution

Given ,

tan $$\begin{bmatrix}\frac{\pi}{2}-\frac{\alpha}{2}\end{bmatrix}=\sqrt{3}$$

cot $$\begin{bmatrix}\frac{\alpha}{2}\end{bmatrix}=\sqrt{3}$$

$$\frac{\alpha}{2}$$ = $$30^{\circ}$$ ( $$\because\ cot\ 30^{\circ} = \sqrt{3}$$)

$$\alpha = 60^{\circ}$$

cos $$\alpha = cos\ 30^{\circ} = \frac{1}{2}$$

Hence, option B is the correct answer.

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