Question

If x = 2 sin 60° cos 60° and y = sin² 30° − cos² 30° and x² = ky², the value of k is ______.

Options

• `sqrt3`

• `-sqrt3`

• 3

• −3

Answer 1

If x = 2 sin 60° cos 60° and y = sin² 30° − cos² 30° and x² = ky², the value of k is 3.

Explanation:

x = 2 sin 60° cos 60°

= `2 xx sqrt3/2 xx 1/2`

= `sqrt3/2`

y = sin² 30° − cos² 30°

= `1/4 - 3/4`

= `(-2)/4`

= `(-1)/2`

Given, x² = ky²

`(sqrt3/2)^2 = k((-1)/2)^2`

`3/4 = k/4`

k = 3