Can someone help me with this trig question please

We know that in Quadrant 1, both sin x and cos x are positive

We are given:

cosec x = √6 / 2

Since Sin x is 1/ cosec x:

Sinx  = 1/cosecx

Sinx = 1/(√6 / 2)

Sinx = 2 /√6

From the pythagoras theorem,

Sin²x + cos²x = 1

Replacing the value of SinΘ

(2 / √6)² + cos²x = 1

4 / 6 + cos²x = 1

cos²x = 1 - (4 / 6)

cos²x = 2 / 6

cosx = √(2 /6)

i think the answer is b