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If $sin θ = 13,$ then which of the following is the value of the expression $2 cot 2 θ + 2$ ?

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answer is C.

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Detailed Solution

Given:

sin θ = 13

We know that,

cosec θ = 1 sin θ

⇒ cosec θ = 113

⇒ cosec θ = 3

Therefore we have,

2 cot 2 θ + 2 = 2 cot 2 θ + 1

⇒ 2 cosec 2 θ ∵ cot 2 θ + 1 = cosec 2 θ ⇒ 2 × 32 ∵ cosec θ = 3 ⇒ 18

Therefore, the value of the expression

2 cot 2 θ + 2 = 18.

Hence, option (3) is correct.

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