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Solve : lim x_0 [ cot 2 θ -csc 2 θ ]

User Newd
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1 Answer

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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

User Santosh Kadam
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