Evaluate the definite integrals `int_0^(pi/2)cos^2x""""dx`

Explanation

Consider `I=\int_{0}^{\pi / 2} \cos ^{2} x d x \quad ` ………………..`(1)`


`I=\int_{0}^{\pi / 2} \cos ^{2}(\frac{\pi}{2}-x) d x \quad(\int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x)`




`I=\int_{0}^{\pi / 2} \sin ^{2} x d x \quad ` ………………………….`(2)`


...