Question Number 210566 by Erico last updated on 12/Aug/24
![Prove that: if (x∈]−(π/2),(π/2)[ y =∫^( x) _( 0) (dt/(cos(t))) ) ⇒ (y∈IR x =∫^( y) _( 0) (dt/(cosh(t))) )](https://www.tinkutara.com/question/Q210566.png)
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{if}\:\left(\mathrm{x}\in\right]−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\left[\:\:\mathrm{y}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{cos}\left(\mathrm{t}\right)}\:\right)\:\Rightarrow\:\:\left(\mathrm{y}\in\mathrm{IR}\:\:\:\mathrm{x}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{y}} \frac{\mathrm{dt}}{\mathrm{cosh}\left(\mathrm{t}\right)}\:\right) \\ $$