Question

The number of distinct solutions of $\sqrt{3}\sec x-\sqrt{3}\tan x=3,0\le x\le 3\pi$ is?

• A. $6$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $6$

REF.image

$\to$ secx - tanx = $\sqrt{3}$

1 - sinx = $\sqrt{3}cosx\Rightarrow 1+si{n}^{2}x-2sinx=3co{s}^{2}x$

$\Rightarrow 1+si{n}^{2}x-2sinx=3-3si{n}^{2}x\Rightarrow 4si{n}^{2}x-sinx-2=0$

$\Rightarrow sinx=\frac{1\pm \sqrt{1+32}}{8}=\frac{1\pm \sqrt{33}}{8}=\frac{1+\sqrt{33}}{8}or\frac{1-\sqrt{33}}{8}$

$\Rightarrow 6$ solutions.