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

$$\underset{-\frac{\pi }{2}}{\stackrel{+\frac{\pi }{2}}{\int }}\frac{\sin x}{\cos x}dx$$$$\underset{-\frac{\pi }{2}}{\stackrel{+\frac{\pi }{2}}{\int }}\frac{\sin x}{\cos x}\cos \left(2nx\right)dx$$$$\underset{-\frac{\pi }{2}}{\stackrel{+\frac{\pi }{2}}{\int }}\frac{\sin x}{\cos x}\sin \left(2nx\right)dx$$$$n\in {\mathbb{N}}^{\ast }$$

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

$${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\frac{\sin x}{\cos x}dx={\int }_{-\frac{\pi }{2}}^0\frac{\sin x}{\cos x}dx+{\int }_0^{\frac{\pi }{2}}\frac{\sin x}{\cos x}dx$$$$\mathrm{both}\mathrm{integral}\mathrm{dont}\mathrm{converge}.$$

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