Question

If x = cos 30° − sin 30° and y = tan 60° − cot 60°, then ______.

Options

• x = y

• x > y

• x < y

• x > 1, y < 1

Answer 1

If x = cos 30° − sin 30° and y = tan 60° − cot 60°, then x < y.

Explanation:

x = cos 30° − sin 30°

= `sqrt3/2 − 1/2`

= `(sqrt3 - 1)/2`

= `0.732/2`

= 0.366

y = tan 60° − cot 60°

= `sqrt3 - 1/sqrt3`

= `2/sqrt3`

= `(2sqrt3)/3`

= `(2 xx 1.732)/3`

= `3.464/3`

= 1.1546 approx.