Question

Area laying between the curves $y=\tan x,y=\cot xandx-axis,x\left[o,\frac{\pi }{2}\right]is$

Answer 1

$A=2{\int }_0^{\pi /4}\tan xdxA=-2{\left[\ln \cos x\right]}_0^{\pi /4}A=-2\left[\ln \cos \pi /4-\ln \cos 0\right]A=-2[\ln \frac{1}{\sqrt{2}}-\ln 1]A=-2\ln \frac{1}{\sqrt{2}}A=2\ln \sqrt{2}A=\ln 2$