Let

On multiplying and dividing (1 – cos x), we can write the integral as

[∵ sin²θ + cos²θ = 1]

[∵ cosec²θ – cot²θ = 1]

Recall and

We also have

⇒ I = –cosec x – (–cot x) + x + c

⇒ I = –cosec x + cot x + x + c

Thus,