if sinθ = \(\frac{1}{3}\) , then find the value of 2 cot2θ + 2.

1.	if sinθ = \(\frac{1}{3}\) , then find the value of 2 cot2θ + 2.
Answer» Given: sinθ = \(\frac{1}{3}\) To find: The value of 2cot²θ + 2. Solution: \(\)sinθ = \(\frac{1}{3}\) ∵ cosecθ = \(\frac{1}{sinθ}\) = \(\frac{1}{1/3}\) = 3 ⇒ cosec²θ = 3² = 9 Also, 1 + cot²θ = cosec²θ ⇒ cot²θ = cosec²θ – 1 = 9 – 1 = 8 ⇒ 2 cot²θ + 2 = 2 (8) + 2 = 16 + 2 = 18 Hence, the value of 2cot²θ + 2 is 18.

Answer»

Given: sinθ = \(\frac{1}{3}\)

To find: The value of 2cot²θ + 2.

Solution: \(\)sinθ = \(\frac{1}{3}\)

∵ cosecθ = \(\frac{1}{sinθ}\) = \(\frac{1}{1/3}\) = 3

⇒ cosec²θ = 3² = 9

Also, 1 + cot²θ = cosec²θ

⇒ cot²θ = cosec²θ – 1 = 9 – 1 = 8

⇒ 2 cot²θ + 2 = 2 (8) + 2 = 16 + 2 = 18

Hence,

the value of 2cot²θ + 2 is 18.

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