Question

If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot² θ + 2. 

Answer 1

Given:  

`sin θ=1/3`

⇒ `1/ sinθ=3` 

⇒` cosec θ=3` 

We know that, 

`cosec^2θ-cot ^2θ=1` 

⇒`(3)^2-cot^2θ=1` 

⇒ `cot ^2 θ=9-1`  

Therefore, 

`2 cot ^2 θ+2=2xx8+2` 

          =`16+2` 

          = `18`