$\int\limits_{π/4}^{3π/4}\frac{dx}{1+cosx}$ is equal to

2 -2 $\frac{1}{2}$ $-\frac{1}{2}$

2

Let $I=\int\limits_{π/4}^{3π/4}\frac{dx}{1+cosx}=\int\limits_{π/4}^{3π/4}\frac{dx}{1-cosx}$ $⇒2I=2\int\limits_{π/4}^{3π/4}\frac{dx}{1-cos^2x}=2\int\limits_{π/4}^{3π/4}cosec^2x\,dx=-2cot\,x|_{π/4}^{3π/4}=4$ $⇒I=2$ Hence (A) is the correct answer.