pi-2-pi-2-sin-x-cos-x-dx-pi-2-pi-2-sin-x-cos-x-cos-2nx-dx-pi-2-pi-2-sin-x-cos-x-sin-2nx-dx-n-N-

Question Number 630 by 123456 last updated on 15/Feb/15

\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} d x

\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} \cos (2 n x) d x

\underset{- \frac{π}{2}}{\int^{+ \frac{π}{2}}} \frac{\sin x}{\cos x} \sin (2 n x) d x

n \in N^{*}

Commented by prakash jain last updated on 15/Feb/15

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin x}{\cos x} d x = \int_{- \frac{π}{2}}^{0} \frac{\sin x}{\cos x} d x + \int_{0}^{\frac{π}{2}} \frac{\sin x}{\cos x} d x

both integral dont converge .