$\int\limits_{π/4}^{3π/4}\frac{dx}{1+cosx}$ is equal to
Answer & explanation
Correct answer: option 1
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.