Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1 ( divide all terms by sin²x )
1 + [tex]\frac{cos^2x}{sin^2x}[/tex] = [tex]\frac{1}{sin^2x}[/tex]
1 + cot²x = csc²x
When cotΘ = 3, then
1 + 3² = csc²Θ
csc²Θ = 10 ( take the square root of both sides )
cscΘ = [tex]\sqrt{10}[/tex]
