First slide

Trigonometric equations

Question

If $2 \tan â¡ (Ï / 3) \cos â¡ (2 Ï x) = \sqrt{3},$ the general solution of the equation is

Moderate

A

$2 n Ï Â\pm \frac{Ï}{3}$
B

$n Â\pm \frac{1}{3}$
C

$n Â\pm \frac{1}{6}$
D

$n Â\pm \frac{1}{2} (n â I)$

Solution

$\begin{array}{l} 2 Ã \sqrt{3} \cos â¡ (2 Ï x) = \sqrt{3} \\ â \cos â¡ (2 Ï x) = 1 / 2 = \cos â¡ (2 n Ï Â\pm Ï / 3) \\ â x = n Â\pm 1 / 6 . \end{array}$

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