Question

If 2 sin A = 1, then the value of tan A + cot A is ______.

Options

• `sqrt(3)`

• `4/sqrt(3)`

• `sqrt(3)/2`

• 1

Answer 1

If 2 sin A = 1, then the value of tan A + cot A is `underlinebb(4/sqrt(3))`.

Explanation:

2 sin A = 1 ⇒ sin A = `1/2`.

We know sin 30° = `1/2`, so A = 30°.

Evaluate: tan 30° + cot 30°.

`tan 30^circ = 1/sqrt(3)` and `cot 30^circ = sqrt(3)`

`1/sqrt(3) + sqrt(3) = (1 + 3)/sqrt(3)`

= `4/sqrt(3)`