Question

Find the principal solution of $ta{n}^{2}x+(\sqrt{3}-1)tanx-\sqrt{3}=0$

• A. $x=\frac{\pi }{4}$
• B. $x=\frac{\pi }{3}$
• C. $x=-\frac{\pi }{4}$
• D. $x=-\frac{\pi }{3}$

Answer 1

Answer: (A), (D)

The correct options are
A

$x=\frac{\pi }{4}$

D

$x=-\frac{\pi }{3}$

$ta{n}^{2}x+(\sqrt{3}-1)tanx-\sqrt{3}=0ta{n}^{2}x-tanx+\sqrt{3}tanx-\sqrt{3}=0tanx(tanx-1)+\sqrt{3}(tanx-1)=0(tanx+\sqrt{3})(tanx-1)=0tanx=-\sqrt{3}ortanx=1x=-\frac{\pi }{3}orx=\frac{\pi }{4}$