if sinθ = 1/3 then find the value of 2 cot^2θ + 2.

Question

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

Answer 1

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.