In NCERT book Ex 7.2 question no.5 I am unable to understand that sin2(ax+b)/2.then we take 2(ax+b)=t but 2adx = dt How and from where the 'a' comes.please explain

We can write sin (ax+ b) cos (ax + b) as sin2(ax+ b)/ 2.

(By using the formula sin 2A = 2 sin A cos A)

 

Now, we substitute 2(ax + b) = t

So, 2ax + 2b = t

Differentiating both sides, we get:

2a dx = dt

 

Now, with this substitution, we can easily integrate the given function.