Find csc x if cotx= - sqrt(15)?

Question

please help!!!!!!!!!!!!!!

Answer 1

cotx  = -sqrt(15)

Square to each side

(cotx)² = [-sqrt(15)]²

cot²X = 15

Recall : cot²X = csc²X -1

Substitue cot²X = csc²X -1

csc²X -1 = 15

Add 1 to each side

csc²X = 15+1

csc²X = 16

cscx =sqrt(16)

Therefore cscx = 4 or cscx =-4