Question

The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.

Options

• `pi/6, pi/12`

• `pi/12, (5pi)/12`

• `pi/8, (3pi)/8`

• `pi/8, pi/4`

Answer 1

The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are `underline((pi/12, (5pi)/12)`.

Explanation:

We have, sin x cos x = `1/4`

⇒ 2 sin x cos x = `1/2`

⇒ sin 2x = `1/2`

⇒ 2x = `sin^-1 (1/2) = pi/6`

⇒ x = `pi/6`

If x ∈ `(0, pi/2)`, then x = `pi/12, pi/2 - pi/12 = pi/12, (5pi)/12`