Question

Evaluate:

(i) ∫1/(1 - cos x) dx

(ii) ∫1/(1 - sin x) dx

Answer 1

(i) ∫1/(1 - cos x) dx

Now multiply and divide by (1 + cos x) 

So we get

= ∫(cosec² x + cosec x cot x) dx

By integrating w.r.t x

= – cot x – cosec x + c

(ii) ∫1/(1 - sin x) dx

Now multiply and divide by (1 + sin x) 

So we get

= ∫(sec² x + sec x tan x) dx

By integrating w.r.t x

= tan x + sec x + c