Question

The area between the curves y = tanx, y = cotx and x - axis in the interval $[0,\pi /2]$ is

• A. $log2$
• B. $log3$
• C. $log\sqrt{2}$
• D. None of these

Answer 1

The correct option is A $log2$

$A=2{\int }_0^{\pi /4}\tan xdx$

$A=2{[-\log \cos x]}_0^{\pi /4}$

$A=2[-\log \cos \pi /4]$$-[-\log \cos 0]$

$A=-2\log \sqrt{1/2}$

$A=\log 2$