Final answer:
To evaluate the given limit lim x->0 (cot 2 -csc 2), we can simplify the expression using trigonometric identities and obtain the answer as 1.
Step-by-step explanation:
The given expression is lim x→0 (cot 2θ - csc 2θ). To evaluate this limit, we can simplify the expression using trigonometric identities:
cot 2θ = 1/tan 2θ = cos^2θ/sin^2θ
csc 2θ = 1/sin 2θ
Substituting these identities into the expression, we get:
lim x→0 [(cos^2θ/sin^2θ) - (1/sin^2θ)]
= lim x→0 [(cos^2θ - 1)/sin^2θ]
= lim x→0 [(1 - sin^2θ)/sin^2θ] (by using the identity cos^2θ = 1 - sin^2θ)
= lim x→0 [(sin^2θ)/sin^2θ]
= lim x→0 1
= 1