Question

If A = 30°, then \[\frac{\sin 2A}{1 - \cos 2A}\] is equal to ______.

Options

• cot A

• tan A

• sec A

• cosec A

Answer 1

If A = 30°, then \[\frac{\sin 2A}{1 - \cos 2A}\] is equal to cot A.

Explanation:

Substituting A = 30° into the expression:

\[\frac{\sin 60^\circ}{1 - \cos 60^\circ} = \frac{\frac{\sqrt{3}}{2}}{1 - \frac{1}{2}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}\]

Since \[\cot 30^\circ = \sqrt{3}\], the expression is equal to cot A.