The value of $$\sqrt{\left(\frac{(4-5 \text{cos}^2⁡θ)}{\text{sin}^2⁡θ} +cot^2⁡θ\right )}$$​ is:

Correct option is C

Given: 

$$\sqrt{\left(\frac{(4-5 \text{cos}^2⁡θ)}{\text{sin}^2⁡θ} +cot^2⁡θ\right )}$$ 

Formula Used: 

Cot²​$$\theta$$ = $$\frac{\text{cos}^2\theta}{\text{sin}^2\theta}$$ 

sin²​$$\theta$$ = 1 - cos²​$$\theta$$​​

Solution: 

$$\sqrt{\left(\frac{(4-5 \text{cos}^2⁡θ)}{\text{sin}^2⁡θ} +\frac{\text{cos}^2⁡θ}{\text{sin}^2\theta}\right )}$$ 

= $$\sqrt{\left(\frac{(4-5 \text{cos}^2⁡θ)+\text{cos}^2⁡θ}{\text{sin}^2\theta}\right )}$$ 

= $$\sqrt{\left(\frac{4-4 \text{cos}^2⁡θ}{\text{sin}^2\theta}\right )}$$

= $$\sqrt{\left(\frac{4(1- \text{cos}^2⁡θ)}{\text{sin}^2\theta}\right )}$$ 

= $$\sqrt{\left(\frac{4(\text{sin}^2⁡θ)}{\text{sin}^2\theta}\right )}$$ 

= $$\sqrt4$$ 

= 2