NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 13

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. Factor the numerator as 2(cos x−cos α)(cos x+cos α); cancel only on the original domain.
3. An antiderivative is F(x)=\(2 x \cos{\left(\alpha \right)} + 2 \sin{\left(x \right)}\).
4. Differentiate this expression to check that F′(x)=\(\frac{- \cos{\left(2 \alpha \right)} + \cos{\left(2 x \right)}}{- \cos{\left(\alpha \right)} + \cos{\left(x \right)}}\). Add an arbitrary constant C on each domain component.