Question

Find the principal solution of $2co{s}^{2}x-3cosx-2=0$

• A. $x=\frac{\pi }{3}$
• B. $x=\frac{2\pi }{3}$
• C. $x=\frac{5\pi }{6}$
• D. no solution

Answer 1

The correct option is B

$x=\frac{2\pi }{3}$

$2co{s}^{2}x-3cosx-2=0$
Let cos x = t
$2t^2-3t-2=0t=\frac{3\pm \sqrt{9-4\times 2\times (-2)}}{2\times 2}t=\frac{3\pm \sqrt{25}}{4}t=2ort=-\frac{1}{2}$

Since cos x cannot be 2, we have
$cosx=-\frac{1}{2}x=\frac{2\pi }{3}$