The integration is of 1/(1-sinx) from 0 to pi/2.
If we go by the approach done on the left, i.e. multiplying and dividing by (1+sinx),and further, we get answer as undefined.
But if we go by the approach done on the right, i.e. conversion to half angles, we get 1/2. The second approach is given in NCERT, but what is wrong in the first one? I feel that the fist one is more accurate, by looking at its graph.
Please tag some guys who you think can help. (I can't as I am still a new user (since a few months lol)