Question Number 131827 by Salman_Abir last updated on 09/Feb/21
Answered by liberty last updated on 09/Feb/21
![= ln ∣tan x∣ ]_(π/4) ^(π/3) = ln ∣tan (π/3)∣−ln ∣tan (π/4)∣ = (1/2)ln (3)](https://www.tinkutara.com/question/Q131830.png)
$$\left.\:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\mathrm{x}\mid\:\right]_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{3}}\mid−\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{4}}\mid \\ $$$$\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left(\mathrm{3}\right) \\ $$