The value of (cosecθ+cotθ)×(1-cosθ)is:

Correct option is C

​Given:

Expression: (cosecθ + cotθ) × (1 - cosθ)

Formula Used:
cosecθ = 1/sinθ and cotθ = cosθ/sinθ
​
Solution:
(cosecθ + cotθ) × (1 - cosθ)
​$$= \left(\frac{1}{\sin\theta} + \frac{\cos\theta}{\sin\theta}\right) \times (1 - \cos\theta) \\= \frac{1 + \cos\theta}{\sin\theta} \times (1 - \cos\theta) \\= \frac{(1 + \cos\theta)(1 - \cos\theta)}{\sin\theta} \\= \frac{1 - \cos^2\theta}{\sin\theta}$$​​
Using the identity 1 - cos²θ = sin²θ, we get:
​$$\frac{\sin^2\theta}{\sin\theta} = \sin\theta$$​​